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Sub 505 (Easy)|   Exponents|   Roots|                                 
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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 Updated on: 22 Jun 2018, 01:29
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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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

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5% (low)

Question Stats:

88% (01:11) correct 12% (01:42) wrong based on 4498 sessions

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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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Official Answer
D
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The function f is defined by f(x) = x^(1/2) - 10 for all positive numb 03 May 2011, 11:18
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IEsailor
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
Show more

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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The function f is defined by f(x) = x^(1/2) - 10 for all positive numb 27 Oct 2015, 06:04
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IEsailor
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. \((u^2 + 10)^2\)
Show more

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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The function f is defined by f(x) = x^(1/2) - 10 for all positive numb 03 May 2011, 15:32
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IEsailor
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
Show more



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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The function f is defined by f(x) = x^(1/2) - 10 for all positive numb 18 Oct 2015, 22:02
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Bunuel
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.
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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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The function f is defined by f(x) = x^(1/2) - 10 for all positive numb 01 Apr 2016, 16:16
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Attached is a visual that should help.
Attachments

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 65576 times ]

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The function f is defined by f(x) = x^(1/2) - 10 for all positive numb 19 Dec 2017, 07:44
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IEsailor
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. \((u^2 + 10)^2\)
Show more

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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The function f is defined by f(x) = x^(1/2) - 10 for all positive numb 08 Mar 2018, 15:09
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IEsailor
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. \((u^2 + 10)^2\)
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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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The function f is defined by f(x) = x^(1/2) - 10 for all positive numb 01 Dec 2019, 21:00
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Bunuel
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) \((u^2 + 10)^2\)
Show more

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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The function f is defined by f(x) = x^(1/2) - 10 for all positive numb 09 Jul 2020, 00:21
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Bunuel
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) \((u^2 + 10)^2\)
Show more

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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The function f is defined by f(x) = x^(1/2) - 10 for all positive numb 12 May 2021, 01:07
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Bunuel
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) \((u^2 + 10)^2\)
Show more

Answer: Option D

Video solution by GMATinsight

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The function f is defined by f(x) = x^(1/2) - 10 for all positive numb 22 Nov 2021, 02:52
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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 27 Jun 2022, 11:45
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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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The function f is defined by f(x) = x^(1/2) - 10 for all positive numb 10 Sep 2025, 03:36
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