Studdy AI Logo
Math  /  Algebra

QuestionEvaluate the indicated function for f(x)=x2+2f(x)=x^{2}+2 and g(x)=x−3g(x)=x-3 (f+g)(2)(f+g)(2)=\begin{array}{c} (f+g)(2) \\ (f+g)(2)= \end{array} Submit Answer

Studdy Solution

STEP 1

1. We are given two functions: f(x)=x2+2 f(x) = x^2 + 2 and g(x)=x−3 g(x) = x - 3 .
2. We need to evaluate the function (f+g)(x) (f+g)(x) at x=2 x = 2 .

STEP 2

1. Define the function (f+g)(x) (f+g)(x) .
2. Substitute x=2 x = 2 into the function (f+g)(x) (f+g)(x) .
3. Calculate the value of (f+g)(2) (f+g)(2) .

STEP 3

Define the function (f+g)(x) (f+g)(x) :
(f+g)(x)=f(x)+g(x) (f+g)(x) = f(x) + g(x)
Substitute the given functions:
(f+g)(x)=(x2+2)+(x−3) (f+g)(x) = (x^2 + 2) + (x - 3)
Combine like terms:
(f+g)(x)=x2+x−1 (f+g)(x) = x^2 + x - 1

STEP 4

Substitute x=2 x = 2 into (f+g)(x) (f+g)(x) :
(f+g)(2)=(2)2+2−1 (f+g)(2) = (2)^2 + 2 - 1

STEP 5

Simplify the expression:
(f+g)(2)=4+2−1 (f+g)(2) = 4 + 2 - 1

STEP 6

Calculate the final value:
(f+g)(2)=6−1 (f+g)(2) = 6 - 1 (f+g)(2)=5 (f+g)(2) = 5
The value of (f+g)(2) (f+g)(2) is:
5 \boxed{5}

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