Question

Find (fºg)(-4) for the following functions.f(x) = 3x – 3 and g(x) = x^2 + 2

Answer 1

WE are givent the functions

`f(x)=3x\text{ -3}`

and

`g(x)=x^2+2`

We want to calculate the following

`f\circ g(\text{ -4)}`

This operation is the function composition. What it means is that first we are going to input -4 into g. Then, the value we get, we input it into f.

So first we calculate

`g(-4)=(-4)^2+2=16+2=18`

Now, we calculate

`f(18)=3\cdot18\text{ -3 =51 }`

So we have that

`f\circ g(\text{ -4)=f(g(-4))=f(18)=51}`