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Math Expert V
Joined: 02 Sep 2009
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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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Difficulty:   5% (low)

Question Stats: 86% (01:12) correct 14% (01:43) wrong based on 1262 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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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.
Retired Moderator Joined: 20 Dec 2010
Posts: 1545
Re: The function f is defined by f(x) = x^(1/2) - 10 for all positive numb  [#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"
##### General Discussion
Manager  Joined: 07 Oct 2010
Posts: 127
Re: The function f is defined by f(x) = x^(1/2) - 10 for all positive numb  [#permalink]

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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^(1/2) - 10 for all positive numb  [#permalink]

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straight D.

t= (u+10) ^2
Manager  Joined: 12 Oct 2009
Posts: 124
Re: The function f is defined by f(x) = x^(1/2) - 10 for all positive numb  [#permalink]

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Thank you guys, Mistook it to be Underroot( t-10 )...Thanks again for all the help
Director  Joined: 01 Feb 2011
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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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t (in terms of u)?

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

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

Intern  Joined: 03 May 2011
Posts: 1
Re: The function f is defined by f(x) = x^(1/2) - 10 for all positive numb  [#permalink]

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1
1
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

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]

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f(t) = root(t) - 10 = u

=> 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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1
ok, so we have f(t) = u
rewrite this as:
sqrt(t) - 10 = u
sqrt(t) = u+10

square everything:
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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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)

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]

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2
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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. $$(u+10)^2 = t$$

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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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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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Originally posted by mcelroytutoring on 01 Apr 2016, 16:10.
Last edited by mcelroytutoring on 01 Apr 2016, 19:28, 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 [ 114.92 KiB | Viewed 18214 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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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

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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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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]

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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) $$(u^2 + 10)^2$$

Just substitute f(x) for u and simplify it Intern  B
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GMAT 1: 760 Q50 V44 GMAT 2: 770 Q51 V44 Re: The function f is defined by f(x) = x^(1/2) - 10 for all positive numb  [#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) $$(u^2 + 10)^2$$

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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