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

1 Answer
Feb 12, 2017

(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.