Math  /  Algebra

QuestionLet f(x)=2x1,g(x)=3xf(x)=2 x-1, g(x)=3 x, and h(x)=x2+1h(x)=x^{2}+1. Find f(h(7))f(h(7))

Studdy Solution

STEP 1

1. We are given three functions: f(x)=2x1 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 f(h(7)) f(h(7)) .

STEP 2

1. Evaluate the function h(x) h(x) at x=7 x = 7 .
2. Use the result from step 1 as the input to the function f(x) f(x) .
3. Evaluate the function f(x) f(x) using the result from step 2.

STEP 3

Evaluate h(7) h(7) :
h(7)=72+1 h(7) = 7^2 + 1

STEP 4

Calculate 72 7^2 and add 1:
h(7)=49+1 h(7) = 49 + 1 h(7)=50 h(7) = 50

STEP 5

Substitute the result from STEP_2 into f(x) f(x) :
f(h(7))=f(50) f(h(7)) = f(50)

STEP 6

Evaluate f(50) f(50) :
f(50)=2(50)1 f(50) = 2(50) - 1

STEP 7

Calculate 2×50 2 \times 50 and subtract 1:
f(50)=1001 f(50) = 100 - 1 f(50)=99 f(50) = 99
The value of f(h(7)) f(h(7)) is:
99 \boxed{99}

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