Question

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

Answer 1

Evaluating Composite Functions

Answer:

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

Step-by-step 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 $w(-22)$:

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