Question

Let f(x) = -4x + 7 and g(x) = 2x - 6. Find (fog)(1).

Answer 1

23

Explanation:

Basically, (f o g)(1) is saying f(g(1))

So let's plug in 1 into the g(x) equation.

`g(1)=2(1)-6 \\ \\ g(1)=2-6 \\ \\ g(1)=-4`

Now we can plug in -4 into the f(x) equation.

`f(-4)=-4(-4)+7 \\ \\ f(-4)=16+7 \\ \\ f(-4)=23`

Answer 2

23

Explanation:

This is a problem of composition of function. We can define this as follows:

`The \ \mathbf{composition} \ of \ the \ function \ f \ with \ the \ function \ g \ is:\\ \\ (f \circ g)(x)=f(g(x)) \\ \\ The \ domain \ of \ (f \circ g) \ is \ the \ set \ of \ all \ x \ in \ the \ domain \ of \ g \\ such \ that \ g(x) \ is \ in \ the \ domain \ of \ f`

So
`(f.g)(x)=f(g(x))=h(x)`:

`h(x)=-4(2x-6)+7 \\ \\ h(x)=-8x+24+7 \\ \\ h(x)=-8x+31`

Therefore:

`h(x)=f(g(1))=-8(1)+31=23`