Exponential Functions

f(x) = log₂(x + 6), find the value of f⁻1(3)

Write the given function as     y = log₂ (x + 6)

Writing this in exponential form, we have

2^y  = x + 6        subtract 6 from both sides

2^y - 6   = x       "swap" x and y

2^x - 6  = y       and, for y, write f^-1(x)

So 

f^-1(x)   = 2^x - 6     and   f^-1(3)  =    2⁽³⁾  - 6    =   8  - 6  = 2

So  the point (3, 2)  is on the inverse graph....then the point (2, 3)  should be on the original graph.....and you can verify for yourself that this is true......