Answer:
[tex]f^{-1}(x) = log_2(x-6)[/tex]
Step-by-step explanation:
To find the inverse [tex]f^{-1}(x)[/tex] of a function follow the following steps.
1) Do y = f (x)
[tex]f(x) =y= 2 ^ x + 6[/tex]
[tex]y= 2 ^ x + 6[/tex]
2) Solve the equation for the variable x.
[tex]y= 2 ^ x + 6\\\\y-6 = 2^x\\\\log_2(y-6) = x\\\\x=log_2(y-6)[/tex]
3) exchange the variable y with the variable x
[tex]x=log_2(y-6)\\\\y=log_2(x-6)[/tex]
Finally the inverse is:
[tex]f^{-1}(x) = log_2(x-6)[/tex]
