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

Question

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

fluke · Accepted Answer

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"

GMATinsight · Answer

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

rossc2 · Answer

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!

v12345 · Answer

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

mcelroytutoring · Answer

Attached is a visual that should help.

ScottTargetTestPrep · Answer

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

SVaidyaraman · Answer

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.

GMATCoachBen · Answer

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

hemantbafna · Answer

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

GMATinsight · Answer

Answer: Option D

Video solution by  GMATinsight

https://www.youtube.com/watch?v=ACGJKBl9990

khera · Answer

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

nookx · Answer

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!

bumpbot · Answer

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

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