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Math  /  Algebra

QuestionCOPY - Let f(x)=2x−1,g(x)=3xf(x)=2 x-1, g(x)=3 x, and h(x)=x2+1h(x)=x^{2}+1. Find h(g(−4))h(g(-4))

Studdy Solution

STEP 1

1. We are given the functions f(x)=2x−1 f(x) = 2x - 1 , g(x)=3x g(x) = 3x , and h(x)=x2+1 h(x) = x^2 + 1 .
2. We need to find the value of h(g(−4)) h(g(-4)) .

STEP 2

1. Evaluate g(−4) g(-4) .
2. Use the result from Step 1 as the input for h(x) h(x) .
3. Evaluate h(g(−4)) h(g(-4)) .

STEP 3

Substitute x=−4 x = -4 into g(x) g(x) :
g(−4)=3(−4) g(-4) = 3(-4)

STEP 4

Simplify the expression:
g(−4)=−12 g(-4) = -12

STEP 5

Use the result from Step 2 as the input for h(x) h(x) . Substitute x=−12 x = -12 into h(x) h(x) :
h(−12)=(−12)2+1 h(-12) = (-12)^2 + 1

STEP 6

Simplify the expression:
h(−12)=144+1 h(-12) = 144 + 1

STEP 7

Complete the simplification:
h(−12)=145 h(-12) = 145
The value of h(g(−4)) h(g(-4)) is:
145 \boxed{145}

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