Chapter SH, Problem 4.21EP

To determine

To find inverse of the function $f(x)=\frac{1}{2}x+7$ .

Answer to Problem 4.21EP

  $f^{-1}(x)=2X-14$

Explanation of Solution

Given information:

The function is $f(x)=\frac{1}{2}x+7$

Calculation:

  $f(x)=\frac{1}{2}x+7$

Replace $f(x)$with Y

  $Y=\frac{1}{2}X+7$

Switch X with Y

  $X=\frac{1}{2}Y+7$

Substract 7 from both sides

So,

  $X-7=\frac{1}{2}Y$

Dividing both sides by $\frac{1}{2}$

  $\frac{X-7}{\frac{1}{2}}=\frac{\frac{1}{2}Y}{\frac{1}{2}}$

So,

  $2X-14=Y$

Then, the inverse function of $f(x)$is given below

  $f^{-1}(x)=2X-14$