Find the equation of the inverse.y = {2}^(x + 5) - 6

Question

Find the equation of the inverse.
`y = {2}^(x + 5) - 6`

Answer 1

Find the equation of the inverse.

`y = {2}^(x + 5) - 6`

we have

`y=\mleft\{2\mright\}^{\mleft\{x+5\mright\}}-6`

step 1

Exchange the variables

x for y and y for x

`x=\{2\}^{\{y+5\}}-6`

step 2

Isolate the variable y

`(x+6)=2^((y+5))`

apply log both sides

`\begin{gathered} \log (x+6)=(y+5)\cdot\log (2) \\ y+5=(\log (x+6))/(\log (2)) \\ \\ y=(\log(x+6))/(\log(2))-5 \end{gathered}`

step 3

Let

`f^((-1))(x)=y`

therefore

the inverse function is

`f^((-1))(x)=(\log(x+6))/(\log(2))-5`