Question

Involves inverse fuctions

Answer 1

Answer:

1. $x$

2. $y$

3.

$y=\dfrac{\ln (x+4)}{2}$

Step-by-step explanation:

Given the function

$f(x)=e^{2x}-4$

To find the inverse function, first change $f(x)$ to $y:$

$y=e^{2x}-4$

Then, switch $x$ and $y:$

$x=e^{2y}-4$

and solve for $y:$

$x+4=e^{2y}\\ \\\ln (x+4)=\ln e^{2y}\\ \\2y=\ln (x+4)\\ \\y=\dfrac{\ln (x+4)}{2}$