CodyWohlfeil
CodyWohlfeil CodyWohlfeil
  • 02-03-2020
  • Mathematics
contestada

Involves inverse fuctions

Involves inverse fuctions class=

Respuesta :

frika
frika frika
  • 10-03-2020

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]

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