Answer:
1. [tex]x[/tex]
2. [tex]y[/tex]
3.
[tex]y=\dfrac{\ln (x+4)}{2}[/tex]
Step-by-step explanation:
Given the function
[tex]f(x)=e^{2x}-4[/tex]
To find the inverse function, first change [tex]f(x)[/tex] to [tex]y:[/tex]
[tex]y=e^{2x}-4[/tex]
Then, switch [tex]x[/tex] and [tex]y:[/tex]
[tex]x=e^{2y}-4[/tex]
and solve for [tex]y:[/tex]
[tex]x+4=e^{2y}\\ \\\ln (x+4)=\ln e^{2y}\\ \\2y=\ln (x+4)\\ \\y=\dfrac{\ln (x+4)}{2}[/tex]
