Studdy AI Logo
Math  /  Algebra

QuestionGiven the functions ff and gg below, find f(g(−1))f(g(-1)). f(x)=−x2+6x+3g(x)=2x+3\begin{array}{l} f(x)=-x^{2}+6 x+3 \\ g(x)=2 x+3 \end{array}
Provide your answer below: f(g(−1))=f(g(-1))=

Studdy Solution

STEP 1

1. We are given two functions: f(x)=−x2+6x+3 f(x) = -x^2 + 6x + 3 and g(x)=2x+3 g(x) = 2x + 3 .
2. We need to find the value of f(g(−1)) f(g(-1)) .

STEP 2

1. Evaluate g(−1) g(-1) .
2. Substitute the result from Step 1 into the function f(x) f(x) .
3. Simplify to find f(g(−1)) f(g(-1)) .

STEP 3

Evaluate g(−1) g(-1) :
g(−1)=2(−1)+3 g(-1) = 2(-1) + 3

STEP 4

Simplify the expression:
g(−1)=−2+3 g(-1) = -2 + 3 g(−1)=1 g(-1) = 1

STEP 5

Substitute g(−1)=1 g(-1) = 1 into f(x) f(x) :
f(g(−1))=f(1) f(g(-1)) = f(1)

STEP 6

Evaluate f(1) f(1) :
f(1)=−(1)2+6(1)+3 f(1) = -(1)^2 + 6(1) + 3

STEP 7

Simplify the expression:
f(1)=−1+6+3 f(1) = -1 + 6 + 3 f(1)=8 f(1) = 8
The value of f(g(−1)) f(g(-1)) is:
8 \boxed{8}

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