Chapter EP, Problem 7.2.7EP

To determine

To calculate: The inverse of the functions $y=-2$ . Also graph the function and its inverse.

Answer to Problem 7.2.7EP

The inverse of the function $y=-2$ does not exist.

Explanation of Solution

Given information:

The functions $y=2x+8$ .

Formula used:

If two functions f and $f^{-1}$ are said to be inverse functions then $f\left(a\right)=b$ if and only if $f^{-1}\left(b\right)=a$ .

Calculation:

Consider the functions $y=-2$ .

Let $f\left(x\right)=y$ .

Interchange the position of x and y ,

  $x=-2$

Evaluate the above equation for y .

No further simplification is possible.

Thus, the inverse of the function $y=-2$ does not exist.