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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)))

User MeV
by
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1 Answer

8 votes
8 votes

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

User Jamie Cook
by
2.7k points
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