Question

Let f(x) = 5x - 4 and g(x) = x^2- 1. Find (g•f)(0).

Answer 1

`(g\cdot f)(0)=4`

Explanation:

So we have the two functions:

`f(x)=5x-4\text{ and } g(x)=x^2-1`

And we want to find:

`(g\cdot f)(0)`

This is the same as:

`=g(0)\cdot f(0)`

So, find g(0) and f(0):

g(0):

Substitute 0 into g(x):

`g(0)=(0)^2-1`

Square:

`g(0)=0-1`

Subtract:

`g(0)=-1`

And f(0):

Substitute 0 into f(x):

`f(0)=5(0)-4`

Multiply:

`f(0)=0-4`

Subtract:

`f(0)=-4`

So, our equation is now:

`(g\cdot f)(0)=g(0)\cdot f(0)=(-1)\cdot(-4)`

Multiply:

`=4`

So, our answer is 4.

And we're done!