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

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The function f is defined by f(x) = √x – 10 for all positive [#permalink]

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

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

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

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

E. \((u^2 + 10)^2\)
[Reveal] Spoiler: OA

Last edited by Bunuel on 18 Jul 2014, 13:28, edited 2 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 – 10 for all positive [#permalink]

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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 – 10 for all positive [#permalink]

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New post 03 May 2011, 10:19
Ans is D

u = f(t) = \sqrt{t} - 10
Therefore, u + 10 = \sqrt{t}
thus, t = \((u + t)^2\)

Hence ans D

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Re: The function f is defined by f(x) = √x – 10 for all positive [#permalink]

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New post 03 May 2011, 10:25
straight D.

t= (u+10) ^2
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Re: The function f is defined by f(x) = √x – 10 for all positive [#permalink]

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New post 03 May 2011, 13:04
Thank you guys, Mistook it to be Underroot( t-10 )...Thanks again for all the help

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Re: The function f is defined by f(x) = √x – 10 for all positive [#permalink]

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New post 03 May 2011, 13:53
t (in terms of u)?

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

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

Answer is D.

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Re: The function f is defined by f(x) = √x – 10 for all positive [#permalink]

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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 – 10 for all positive [#permalink]

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New post 05 May 2011, 06:05
f(t) = root(t) - 10 = u

=> 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 [#permalink]

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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) (u2 + 10)^2

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Re: The function f is defined by f(x) = x^(1/2) – 10 for all positive [#permalink]

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ok, so we have f(t) = u
rewrite this as:
sqrt(t) - 10 = u
sqrt(t) = u+10

square everything:
t=(u+10)^2
answer choice D

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Re: The function f is defined by f(x) = x^(1/2) – 10 for all positive [#permalink]

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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


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Re: The function f is defined by f(x) = √x – 10 for all positive [#permalink]

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

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New post 01 Apr 2016, 15:10
The function f is defined by f(x) = \(\sqrt{x} - 10\) for all positive numbers . If u = f(t) for some positive numbers t and u, what is t in terms of u?
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Last edited by mcelroytutoring on 01 Apr 2016, 18:28, edited 1 time in total.

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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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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 5570 times ]


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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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From the stem you clearly see it is a function question, further you read the phrase "in terms of", which should make you thinking that you should do math instead of plugging in numbers.
Now when you follow the stem you get: f(x) = x√−10, leading to if you plug in t for x: f(t)=√t –10, which is equal to u.
√t –10 = u, add the 10 to both sides and square both sides
--> t = (u+10)^2

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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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New post 19 Dec 2017, 06:44
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] 19 Dec 2017, 06:44
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