Question

how do i find the inverse of e^2x - 3?

Answer 1

does it become ln(e^2x)= ln -3

2x = ln-3

x = ln-3/2 ???

Answer 2

\[e ^{2x}-3 \rightarrow e ^{2x}=3 \rightarrow \ln(3) = 2x \rightarrow \frac{ \ln(3) }{ 2 }=x\]

Answer 3

let me know if that is right, I'm not sure if it is because changed the expression into an equation.

Answer 4

it seems right so the inverse is f^(-1) = ln3/2 ?

Answer 5

i need to find the domaine and range of both f ( x) and f ^ -1 x how do i do that with a logarithium

Answer 6

Possibly, but I'm having doubts it's correct, because I assumed the expression equalled zero but changing it into an equation which I think is incorrect.

Answer 7

the equation is find the inverse of f (x) = e^2x - 3

Answer 8

+ both domain and ranges?

Answer 9

is it the first or second expression here? \[e ^{2x}-3, e ^{2x-3}\]

Answer 10

first

Answer 11

ok

Answer 12

is our answer correct for the inverse?

Answer 13

no I just used wolfram and it is \[\frac{ \ln(x+3) }{ 2 }\]

Answer 14

how would you write it out if you were solving it for the inverse?

Answer 15

\[y = e ^{2x}-3 \rightarrow x= e ^{2y}-3 \rightarrow x+3 = e ^{2y} \rightarrow \ln(x+3) = 2y \rightarrow \frac{ \ln(x+3) }{ 2 }=y\]

Answer 16

So to compute the inverse, you have to do a trick initially where you switch the x and y variables. Once they're switched you solve for y.