easy- medium OG 2016 #63

[danielheulensen]

any better explanations other than the book?

#63 OG 2016 Problem Solving


63. The function f is defined by f(x) = rootx -10 for all positive numbers x. If u =f(t) for some positive numbers t and u, what is t in terms of u?

[GMATGuruNY]

When you post a problem, please include the answer choices.



Let t = 4.
Then u = f(t) = √t - 10 = √4 - 10 = 2 - 10 = -8.
The question stem asks for the value of t=4. This is our target.
Now plug u=-8 into the answer choices to see which yields our target value of 4.
Only D works:
(u + 10)² = (-8 + 10)² = 2² = 4.

The correct answer is D.

[Ian Stewart]

f(x) = √x - 10

To find f(t), just replace 'x' with 't' on the right side above:

f(t) = √t - 10

We know u = f(t) so

u = √t - 10
u + 10 = √t
(u + 10)^2 = t

[Jay@ManhattanReview]

The correct answer is D.

We know that f(x) = √x - 10

=> f(t) = √t - 10; replacing x with t

=> u = √t - 10; it is gven that u = f(t)

=> √t = u + 10

=> t = (u +10)^2; squaring both the sides

The correct answer: D

Hope this helps!

-Jay

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[danielheulensen]

Thanks everyone!

[Scott@TargetTestPrep]

any better explanations other than the book?

#63 OG 2016 Problem Solving


63. The function f is defined by f(x) = rootx -10 for all positive numbers x. If u =f(t) for some positive numbers t and u, what is t in terms of u?

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: (u + 10)^2