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Math  /  Algebra

QuestionLet f(x)=3x−1f(x)=3 x-1 and g(x)=x2+4g(x)=x^{2}+4 Find (f∘g)(1)(f \circ g)(1)
Then (f∘g)(1)=(f \circ g)(1)= □\square (Simplify your answer.)

Studdy Solution

STEP 1

1. We are given two functions f(x)=3x−1 f(x) = 3x - 1 and g(x)=x2+4 g(x) = x^2 + 4 .
2. We need to find the composition of these functions, specifically (f∘g)(1) (f \circ g)(1) .
3. The composition (f∘g)(x) (f \circ g)(x) means applying g(x) g(x) first and then applying f f to the result.

STEP 2

1. Evaluate g(1) g(1) .
2. Use the result from Step 1 to evaluate f(g(1)) f(g(1)) .

STEP 3

Evaluate g(1) g(1) using the function g(x)=x2+4 g(x) = x^2 + 4 .
g(1)=12+4=1+4=5 g(1) = 1^2 + 4 = 1 + 4 = 5

STEP 4

Now use the result from Step 1 to evaluate f(g(1))=f(5) f(g(1)) = f(5) using the function f(x)=3x−1 f(x) = 3x - 1 .
f(5)=3(5)−1=15−1=14 f(5) = 3(5) - 1 = 15 - 1 = 14
The value of (f∘g)(1) (f \circ g)(1) is:
14 \boxed{14}

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