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

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

OA D

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Official Guide

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

OA D
f(x) = √x - 10
So, f(t) = √t - 10

So, if u = f(t), then we can write: u = √t - 10
Add 10 to both sides: u + 10 = √t
Square both sides: (u + 10)^2 = (√t)^2
Simplify right side: (u + 10)^2 = t

Answer: D
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