Chapter 2.5, Problem 49AYU

To determine

To find: The domain and range of then function $h\left(x\right)=\frac{1}{2x}$ and verify the result using graph.

Answer to Problem 49AYU

Domain: $D:\left(-\infty ,\infty \right)-\left\{0\right\}$

Range: $R:\left(-\infty ,\infty \right)-\left\{0\right\}$

Explanation of Solution

Given: $h\left(x\right)=\frac{1}{2x}$

The given function, $h\left(x\right)=\frac{1}{2x}$

This is inverse function. The parent function is $f\left(x\right)=\frac{1}{x}$

The function vertical stretch by factor of 2.

Domain: $D:\left(-\infty ,\infty \right)-\left\{0\right\}$

Range: $R:\left(-\infty ,\infty \right)-\left\{0\right\}$

Now verify using graph.