Question

If f(x)=log2(x+4), what is f^-1(3)?

Answer 1

$f(x)=\log_2(x+4)\\ y=\log_2(x+4)\\ 2^y=x+4\\ x=2^y-4\\ f^{-1}(x)=2^x-4\\\\ f^{-1}(3)=2^3-4=8-4=4$

Answer 2

$f\left( x \right) =\log _{ 2 }{ \left( x+4 \right) } \\ \\ \log _{ 2 }{ \left( x+4 \right) } =y\\ \\ { 2 }^{ y }=x+4$

$\\ \\ x={ 2 }^{ y }-4\\ \\ \therefore \quad { f }^{ -1 }\left( x \right) ={ 2 }^{ x }-4\\ \\ \therefore \quad { f }^{ -1 }\left( 3 \right) ={ 2 }^{ 3 }-4=4$