Math  /  Algebra

Questionf(x)=2x7;g(x)=x2+4f(x)=2 x-7 ; g(x)=x^{2}+4
Select the correct choice below and, if necessary, fill in the answ A. (gf)(1)=(g \circ f)(1)= \square (Simplify your answer.) B. The solution is not defined.

Studdy Solution

STEP 1

1. The problem involves function composition, specifically (gf)(x) (g \circ f)(x) .
2. The function f(x)=2x7 f(x) = 2x - 7 is a linear function.
3. The function g(x)=x2+4 g(x) = x^2 + 4 is a quadratic function.
4. We need to evaluate (gf)(1) (g \circ f)(1) , which means substituting f(1) f(1) into g(x) g(x) .

STEP 2

1. Evaluate f(1) f(1) .
2. Substitute the result from Step 1 into g(x) g(x) .
3. Simplify the expression to find (gf)(1) (g \circ f)(1) .

STEP 3

Evaluate f(1) f(1) using the function f(x)=2x7 f(x) = 2x - 7 :
f(1)=2(1)7 f(1) = 2(1) - 7 f(1)=27 f(1) = 2 - 7 f(1)=5 f(1) = -5

STEP 4

Substitute f(1)=5 f(1) = -5 into g(x)=x2+4 g(x) = x^2 + 4 :
g(5)=(5)2+4 g(-5) = (-5)^2 + 4

STEP 5

Simplify the expression g(5) g(-5) :
g(5)=25+4 g(-5) = 25 + 4 g(5)=29 g(-5) = 29

STEP 6

The value of (gf)(1) (g \circ f)(1) is 29 \boxed{29} .
The correct choice is A: (gf)(1)=29 (g \circ f)(1) = 29 .

Was this helpful?

Studdy solves anything!

banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord