Question

How do you find the inverse of `y=log_4( x/2 +3 )`?

Answer 1

x = 2(`4^y-3)`

Explanation:

Raise both sides to the power of the base of the logarithm, 4
Use `4^log (x/2+3)`= `x/2+3`...
`4^y=x/2+3`.

Answer 2

The inverse of a function can be found algebraically by switching the x and y values and solving for y.

Explanation:

`y = log_4(x/2 + 3)`

`x = log_4(y/2 + 3)`

`4^x = y/2 + 3`

`4^x - 3 = y/2`

`2(4^x - 6) = y`

`2(4^x) - 12 = y`

So, `f^-1(x) = 2(4^x) - 12`. Note the `f^-1(x)`: this is important because it shows efficiently and clearly that this is an inverse function. I have been docked marks before for not including this element in my answer.

Practice exercises:

1. Find the equation of the inverse function.

a). `g(x) =3^(x - 2) + 4`

b). `h(x) =2 log_2(3x - 1)`

Good luck!