Studdy AI Logo
Math  /  Algebra

QuestionGiven f(x)=7xf(x)=7 x and g(x)=7x2+9g(x)=7 x^{2}+9, find the following expressions. (a) (f∘g)(4)(f \circ g)(4) (b) (g∘f)(2)(g \circ f)(2) (c) (f∘f)(1)(f \circ f)(1) (d) (g∘g)(0)(g \circ g)(0) (a) (f∘g)(4)=847(f \circ g)(4)=847 \quad (Simplify your answer.) (b) (g∘f)(2)=(g \circ f)(2)= □\square (Simplify your answer.)

Studdy Solution

STEP 1

1. We are given two functions: f(x)=7x f(x) = 7x and g(x)=7x2+9 g(x) = 7x^2 + 9 .
2. We need to find the compositions of these functions for specific values of x x .

STEP 2

1. Calculate (f∘g)(4)(f \circ g)(4).
2. Calculate (g∘f)(2)(g \circ f)(2).
3. Calculate (f∘f)(1)(f \circ f)(1).
4. Calculate (g∘g)(0)(g \circ g)(0).

STEP 3

Calculate (f∘g)(4)(f \circ g)(4):
First, find g(4) g(4) :
g(4)=7(4)2+9 g(4) = 7(4)^2 + 9

STEP 4

Simplify g(4) g(4) :
g(4)=7(16)+9 g(4) = 7(16) + 9 g(4)=112+9 g(4) = 112 + 9 g(4)=121 g(4) = 121

STEP 5

Now find f(g(4))=f(121) f(g(4)) = f(121) :
f(121)=7×121 f(121) = 7 \times 121

STEP 6

Simplify f(121) f(121) :
f(121)=847 f(121) = 847

STEP 7

Calculate (g∘f)(2)(g \circ f)(2):
First, find f(2) f(2) :
f(2)=7×2 f(2) = 7 \times 2

STEP 8

Simplify f(2) f(2) :
f(2)=14 f(2) = 14

STEP 9

Now find g(f(2))=g(14) g(f(2)) = g(14) :
g(14)=7(14)2+9 g(14) = 7(14)^2 + 9

STEP 10

Simplify g(14) g(14) :
g(14)=7(196)+9 g(14) = 7(196) + 9 g(14)=1372+9 g(14) = 1372 + 9 g(14)=1381 g(14) = 1381
The value of (g∘f)(2)(g \circ f)(2) is:
1381 \boxed{1381}

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