Chapter 5.2, Problem 81AYU

To determine

To Find: A function y = f(x) is increasing on the interval [ 0, 5 ]. What conclusions can you draw about the graph of y = f-1 ( x )?

Answer to Problem 81AYU

Solution:

We can conclude that the function f is increasing on the interval [ f(0), f(5)].

Explanation of Solution

Given:

A function y = f(x) is increasing on the interval [ 0, 5 ].

Calculation:

Let $y=f\left(x\right)$ be increasing on [0, 5].

  

  

• The set of all order pairs $\left(x, f\left(x\right)\right)$ lies on First quadrant
• Both $x$ and $f\left(x\right)$ are positive values
• The set of all reverse order pairs $\left(f\left(x\right), x\right)$ lies on same first quadrant

Therefore, $y=f^{-1}\left(x\right)$ is increasing on f([0, 5])

Let $y=f\left(x\right)$ be increasing on [0, 5].

Therefore, the function f is increasing on the interval [ f(0), f(5)].

  $y=f^{-1}\left(x\right)$ is increasing on $f\left( \left[0, 5\right]\right)$