Question

Determine the equation of the inverse of y = e x + 3 - 4

Answer 1

ANSWER

${f}^{ - 1} (x) = ln(x + 4) - 3$

EXPLANATION

We want to find the equation of the inverse of

$y = {e}^{x + 3} - 4$

First, we need to interchange x and y.

$x= {e}^{y + 3} - 4$

Solve for y,

$x + 4={e}^{y + 3}$

Take the natural logarithm of both sides,

$ln(x + 4)= ln{e}^{y + 3}$

Simplify

$ln(x + 4)= y + 3$

$ln(x + 4) - 3= y$

Hence the inverse function is,

${f}^{ - 1} (x) = ln(x + 4) - 3$