Question

What are the values of h and k ?

Given `f(x) = 4x + h` and `f^-1 (x) = 5 - kx` , where `h` and `k` are constants. Find the values of `h` and `k` .

Answer 1

`h=-20` and `k=-1/4`.

Explanation:

If `f(x)=ax+b`, then `x=1/a(f(x)-b)=1/af(x)-b/a`

Hence for `f(x)=ax+b`, we have `f^(-1)=1/ax-b/a`

Here we have `f(x)=4x+h`, so we should have `f^(-1)(x)=x/4-h/4`

But as `f^(-1)(x)=5-kx`, we have

`-k=1/4` i.e. `k=-1/4` and `-h/4=5` i.e. `h=-20`.