Question

If `f(x) = x^2 - 6` and `g(x) = 2^x - 1`, how do you find the value of `(g*f)(-3)`?

Answer 1

`(g.f)(-3)=7`

Explanation:

Let's write down the functions.
`f(x)=x^2-6` and `g(x)=2^x-1`

Given we are to find what `(g.f)(-3)` is

Now, for any two functions, it's seen that `(g.f)(x)\impliesg(f(x))`

So, to solve this, we have to first find the value of `f(x)` at `x` and then substitute that value for `y` in `g(y)`.

`f(x)=x^2-6` is what we know. They've asked us to find it at `x=-3`.
That makes it `f(-3)=(-3)^2-6=9-6=3`
So `f(-3)=3`

Take it as `y` implying `y=3`
We are now to substitute `y` in `g(y)=2^x-1`
This means `g(3)=2^3-1`

The rest is just easy.