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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)=(f \circ g)(4)= □\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 inputs.

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

To find (f∘g)(4) (f \circ g)(4) , we first need to evaluate g(4) g(4) .
g(x)=7x2+9 g(x) = 7x^2 + 9
Substitute x=4 x = 4 :
g(4)=7(4)2+9 g(4) = 7(4)^2 + 9

STEP 4

Simplify the expression for 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, substitute g(4)=121 g(4) = 121 into f(x) f(x) to find f(g(4)) f(g(4)) :
f(x)=7x f(x) = 7x
Substitute x=121 x = 121 :
f(121)=7(121) f(121) = 7(121)

STEP 6

Calculate f(121) f(121) :
f(121)=847 f(121) = 847
The value of (f∘g)(4) (f \circ g)(4) is:
847 \boxed{847}

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