Question

Use the following function to find the value of each operation.

f(x)=3x-1 m(x)=-4x+1 w(x)= x^2-5x-1

Find. w(f(m(2)))

Answer 1

Evaluating Composite Functions

Answer:

`w(f(m(2))) = 593`

Explanation:

We can write how
`w(f(m(x)))` will be defined but that's too much work and it's only useful when we are evaluating
`w(f(m(x)))` with many inputs.

First let's solve for
`m(2)` first. As you read through this answer, you'll get the idea of what I'm doing.

Given:

`m(x) = -4x +1`

Solving for
`m(2)`:

`m(2) = -4(2) +1 \\ m(2) = -8 +1 \\ m(2) = -7`

Now we can solve for
`f(m(2))`, since
`m(2) = -7`,
`f(m(2)) = f(-7)`.

Given:

`f(x)=3x-1`

Solving for
`f(-7)`:

`f(-7)=3(-7)-1 \\ f(-7) = -21 -1 \\ f(-7) = -22`

Now we are can solve for
`w(-22)`. By now you should get the idea why
`w(f(m(2))) = w(-22)`.

Given:

`w(x) = x^2 -5x -1`

Solving for
`w(-22)`:

`w(-22) = (-22)^2 -5(-22) -1 \\ w(-22) = 484 -5(-22) -1 \\ w(-22) = 484 +110 -1 \\ w(-22) = 593`