Question

Whats the inverse of f(x) = 4^x+2x

Answer 1

• y=4^x+2x

Interchange x and y

`\\ \rm\Rrightarrow x=4^y+2y`

Find y

`\\ \rm\Rrightarrow 4^y=(x)/(2y)`

take log on both

`\\ \rm\Rrightarrow ln4^y=ln(x)/(2y)`

`\\ \rm\Rrightarrow yln4=lnx-ln2y`

`\\ \rm\Rrightarrow yln4-ln2y=lnx`

`\\ \rm\Rrightarrow yln4-ln2-lny=lnx`

`\\ \rm\Rrightarrow yln4-lny=lnx+ln2`

Inverse not possible to find