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The function f is defined by f(x) = x^(1/2) - 10 for all positive numb

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Bunuel
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The function f is defined by f(x) = x^(1/2) - 10 for all positive numb [#permalink] New post   Updated on: 22 Jun 2018, 01:29
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The function f is defined by \(f(x) = \sqrt{x}– 10\) for all positive numbers x. If u = f(t) for some positive numbers t and u, what is t in terms of u?


(A) \(\sqrt{\sqrt{u}+10}\)

(B) \((\sqrt{u}+10)^2\)

(C) \(\sqrt{u^2+10}\)

(D) \((u + 10)^2\)

(E) \((u^2 + 10)^2\)
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D

Originally posted by Bunuel on 03 May 2011, 10:00.
Last edited by Bunuel on 22 Jun 2018, 01:29, edited 3 times in total.
Renamed the topic, edited the question and added the OA.
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Re: The function f is defined by f(x) = x^(1/2) - 10 for all positive numb [#permalink] New post   03 May 2011, 11:18
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IEsailor wrote:
Looks like a simple question but somehow the answer that i am getting is not in the choices provided below ( or so i think ). Pls help

The function f is defined by f(x) = √x – 10 for all positive numbers x. If u = f(t) for some positive
numbers t and u. What is t in terms of u?

A. √(u+10)
B. (√u + 10)^2
C. √(u2+10)
D. (u + 10)^2
E. (u2 + 10)^2


Sol:

\(f(x)=\sqrt{x} \hspace{2}- \hspace{2} 10\)

For x=t,
\(f(t)=\sqrt{t}-10\)

Given:
\(f(t)=u\)

Thus,
\(\sqrt{t}-10=u\)

\(\sqrt{t}=u+10\)

Squaring both sides:
\(t=(u+10)^2\)

Ans: "D"
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Re: The function f is defined by f(x) = x^(1/2) - 10 for all positive numb [#permalink] New post   27 Oct 2015, 06:04
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IEsailor wrote:
The function f is defined by \(f(x) = \sqrt{x} -10\) for all positive numbers x. If u = f(t) for some positive numbers t and u. What is t in terms of u?

A. \(\sqrt{u+10}\)

B. \((\sqrt{u} + 10)^2\)

C. \(\sqrt{u^2+10}\)

D. \((u + 10)^2\)

E. \((u^2 + 10)^2\)


Just a motivation bosster for people afraid of Functions.

Questions of Function generally require the test taker to be only obedient instead of asking them to be smart in Quant.

Just follow the instructions mwnioned in question

Given : f(x)= \(\sqrt{x} -10\)
And u = f(t)

Instruction is to compare f(x) with f(t) and find f(t) I.e. replace x by t in the expression of f(x)

I.e. f(t)= \(\sqrt{t} -10\)
But u = f(t)
I.e. u = \(\sqrt{t} -10\)
I.e. u+10 =\(\sqrt{t}\)
I.e. \((u+10)^2 = t\)

Answer: Option D
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Re: The function f is defined by f(x) = x^(1/2) - 10 for all positive numb [#permalink] New post   03 May 2011, 15:32
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IEsailor wrote:
Looks like a simple question but somehow the answer that i am getting is not in the choices provided below ( or so i think ). Pls help

The function f is defined by f(x) = √x – 10 for all positive numbers x. If u = f(t) for some positive
numbers t and u. What is t in terms of u?

A. √(u+10)
B. (√u + 10)^2
C. √(u2+10)
D. (u + 10)^2
E. (u2 + 10)^2




This problem may seem confusing at first glance with all the variables thrown at you. Here is how I solved this problem:

You are given main function: f(x) = \sqrt{x} - 10
Then, it says "u = f(t)", which basically says "u = f(x)" and "t = x" in your main function
So, from the information provided, you can rewrite the equation to be the following: u = \sqrt{t} - 10
Finally, you are asked "what is t in terms of u?". Basically, solve for t.

u = \sqrt{t} - 10
u + 10 = \sqrt{t}
(u + 10)^2 = t

Answer: D


Hope this helps!
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Re: The function f is defined by f(x) = x^(1/2) - 10 for all positive numb [#permalink] New post   18 Oct 2015, 22:02
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Bunuel wrote:
The function f is defined by \(f(x) = \sqrt{x}– 10\) for all positive numbers x. If u = f(t) for some positive numbers t and u, what is t in terms of u?

(A) \(\sqrt{\sqrt{u}+10}\)
(B) \((\sqrt{u}+10)^2\)
(C) \(\sqrt{u^2+10}\)
(D) (u + 10)^2
(E) (u2 + 10)^2

Kudos for a correct solution.


given \(f(x) = \sqrt{x}– 10\)
and \(u = f(t) = \sqrt{t}– 10\)
=> \(u = \sqrt{t}– 10\)
=> \(u + 10 = \sqrt{t}\)
=> \((u + 10)^2 = t\) (square both sides)

Answer Choice D


kudos, if you like the post
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Re: The function f is defined by f(x) = x^(1/2) - 10 for all positive numb [#permalink] New post   01 Apr 2016, 16:16
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Attached is a visual that should help.
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Screen Shot 2016-04-01 at 4.02.28 PM.png
Screen Shot 2016-04-01 at 4.02.28 PM.png [ 114.92 KiB | Viewed 53387 times ]

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Re: The function f is defined by f(x) = x^(1/2) - 10 for all positive numb [#permalink] New post   19 Dec 2017, 07:44
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IEsailor wrote:
The function f is defined by \(f(x) = \sqrt{x} -10\) for all positive numbers x. If u = f(t) for some positive numbers t and u. What is t in terms of u?

A. \(\sqrt{u+10}\)

B. \((\sqrt{u} + 10)^2\)

C. \(\sqrt{u^2+10}\)

D. \((u + 10)^2\)

E. \((u^2 + 10)^2\)


We are given the function defined by f(x) = √x – 10 and we also see that f(t) = u. First, let's determine what f(t) looks like and then set the result equal to u.

f(t) = √t – 10

√t – 10 = u

To finish, we need to get t in terms of u.

√t = u + 10

t = (u + 10)^2

Answer: D
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Re: The function f is defined by f(x) = x^(1/2) - 10 for all positive numb [#permalink] New post   08 Mar 2018, 15:09
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IEsailor wrote:
The function f is defined by \(f(x) = \sqrt{x} -10\) for all positive numbers x. If u = f(t) for some positive numbers t and u. What is t in terms of u?

A. \(\sqrt{u+10}\)

B. \((\sqrt{u} + 10)^2\)

C. \(\sqrt{u^2+10}\)

D. \((u + 10)^2\)

E. \((u^2 + 10)^2\)

Main Idea: Express what is given in terms of u and t
Details: f(t)=u=root(t)-10
=> (u+10)^2=t
Hence D.
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Re: The function f is defined by f(x) = x^(1/2) - 10 for all positive numb [#permalink] New post   01 Dec 2019, 21:00
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Bunuel wrote:
The function f is defined by \(f(x) = \sqrt{x}– 10\) for all positive numbers x. If u = f(t) for some positive numbers t and u, what is t in terms of u?


(A) \(\sqrt{\sqrt{u}+10}\)

(B) \((\sqrt{u}+10)^2\)

(C) \(\sqrt{u^2+10}\)

(D) \((u + 10)^2\)

(E) \((u^2 + 10)^2\)


f(t) = \(\sqrt{t}\) - 10 (We are just plugging in t wherever x appears in the function; this is how functions work. The part inside the parentheses is the input -- for example, f(3z) = \(\sqrt{3z}\) - 10 )

Now, the question asks "what is t" -- meaning we need to get t alone

u = \(\sqrt{t}\) - 10

u + 10 = \(\sqrt{t}\)

Now, we square both sides:

\((u+10)^2\) = t ---> Answer is D
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Re: The function f is defined by f(x) = x^(1/2) - 10 for all positive numb [#permalink] New post   09 Jul 2020, 00:21
Bunuel wrote:
The function f is defined by \(f(x) = \sqrt{x}– 10\) for all positive numbers x. If u = f(t) for some positive numbers t and u, what is t in terms of u?


(A) \(\sqrt{\sqrt{u}+10}\)

(B) \((\sqrt{u}+10)^2\)

(C) \(\sqrt{u^2+10}\)

(D) \((u + 10)^2\)

(E) \((u^2 + 10)^2\)


Given the \(f(x) = \sqrt{x}– 10\).
When u = f(t);
f(t)=\sqrt{t} - 10
\sqrt{t} - 10=u
\sqrt{t}=u+10
t=(u+10)^2

D
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Re: The function f is defined by f(x) = x^(1/2) - 10 for all positive numb [#permalink] New post   12 May 2021, 01:07
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Bunuel wrote:
The function f is defined by \(f(x) = \sqrt{x}– 10\) for all positive numbers x. If u = f(t) for some positive numbers t and u, what is t in terms of u?


(A) \(\sqrt{\sqrt{u}+10}\)

(B) \((\sqrt{u}+10)^2\)

(C) \(\sqrt{u^2+10}\)

(D) \((u + 10)^2\)

(E) \((u^2 + 10)^2\)


Wanna make solving the Official Questions interesting???


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Answer: Option D

Video solution by GMATinsight



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Re: The function f is defined by f(x) = x^(1/2) - 10 for all positive numb [#permalink] New post   14 Oct 2021, 20:32
Bunuel wrote:
The function f is defined by \(f(x) = \sqrt{x}– 10\) for all positive numbers x. If u = f(t) for some positive numbers t and u, what is t in terms of u?


(A) \(\sqrt{\sqrt{u}+10}\)

(B) \((\sqrt{u}+10)^2\)

(C) \(\sqrt{u^2+10}\)

(D) \((u + 10)^2\)

(E) \((u^2 + 10)^2\)


How do you know that u should go where x is?
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Re: The function f is defined by f(x) = x^(1/2) - 10 for all positive numb [#permalink] New post   22 Nov 2021, 02:52
The question can be answered by solving
u = ✓t -10 fort in terms of u. Adding 10 to both
sides of this equation gives u + 10 = ✓t. Squaring
both sides of the last equation gives (u + 10)2 = t,
which gives t in terms of u
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The function f is defined by f(x) = x^(1/2) - 10 for all positive numb [#permalink] New post   27 Jun 2022, 11:45
Hi all!

I tried to plug in a number that works and chose (E). Why is my reasoning wrong?

f(t)= t^(1/2) -10
f(121)=11-10 = 1 = u

Many thanks!!
_______________________________________

UPDATE:
For the plug-in numbers method I do see now that while 121 works for (E), 144 and 169 do not. How should I have used this method without making careless mistakes? Or is there any, to me invisible, red flag that I should not use the plug-in numbers method?

Thanks!
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Re: The function f is defined by f(x) = x^(1/2) - 10 for all positive numb [#permalink] New post   28 Aug 2023, 05:39
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Re: The function f is defined by f(x) = x^(1/2) - 10 for all positive numb [#permalink]
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