Find the equation of the inverse.
[tex]y = {2}^{x + 5} - 6[/tex]
we have
[tex]y=\mleft\{2\mright\}^{\mleft\{x+5\mright\}}-6[/tex]step 1
Exchange the variables
x for y and y for x
[tex]x=\{2\}^{\{y+5\}}-6[/tex]step 2
Isolate the variable y
[tex](x+6)=2^{(y+5)}[/tex]apply log both sides
[tex]\begin{gathered} \log (x+6)=(y+5)\cdot\log (2) \\ y+5=\frac{\log (x+6)}{\log (2)} \\ \\ y=\frac{\log(x+6)}{\log(2)}-5 \end{gathered}[/tex]step 3
Let
[tex]f^{(-1)}(x)=y[/tex]therefore
the inverse function is
[tex]f^{(-1)}(x)=\frac{\log(x+6)}{\log(2)}-5[/tex]