{ {4e}^(f(x)) }^( - 1) = x - 2 help. how to find f(x) inverse

Question

`{ {4e}^(f(x)) }^( - 1) = x - 2`
help. how to find f(x) inverse

Answer 1

Given function is,

`4e^{f(x)^(-1)} =x-2`
We need to find
`f(x)^(-1)`. So, we need to isolate
`f(x)^(-1) .`
Hence, the first step is to remove 4 from the left side. So, multiply each sides by 4. Therefore,

`\frac{4e^{f(x)^(-1)}}{4} =(x-2)/(4)`

`e^{f(x)^(-1)} = (x-2)/(4)`
Next step is to take natural log ln to each sides of the equation to get rid of f(x)^-1 from the exponent. So,

`n e^{f(x)^(-1)} = ln (x-2)/(4)` Since
`ln e^x = x`

`{f(x)^(-1)} = ln (x-2)/(4)`
So,
`{f(x)^(-1)} = ln (x-2)/(4)`