Let f:(0,infty)to(0,infty) be a uniformly continuous function. Define g:(0,infty)to(0,infty) by g(x)=begincasesx^2 & if 0<xle1, x & if x1.endcases Which of the following statements is true?

(D) Both fcirc g and gcirc f are uniformly continuous.

Q25Section B (Part B)25 of 120

Uniform continuity — compositions with a piecewise power

Let $f:(0,\infty)\to(0,\infty)$ be a uniformly continuous function. Define $g:(0,\infty)\to(0,\infty)$ by

$g(x)=\begin{cases}x^2 & \text{if }0<x\le1,\ x & \text{if }x>1.\end{cases}$

Which of the following statements is true?

Pick an option to check your answer.

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