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QuestionCalculate (a) f(g(0))f(g(0)) and (b) g(f(0))g(f(0)) for f(x)=2x+9f(x)=2x+9 and g(x)=6−x2g(x)=6-x^2.

Studdy Solution

STEP 1

Assumptions1. The function f(x)f(x) is given by f(x)=x+9f(x)=x+9 . The function g(x)g(x) is given by g(x)=6−xg(x)=6-x^{}

STEP 2

To find f(g(0))f(g(0)), we first need to find the value of g(0)g(0).
g(0)=6−(0)2g(0) =6 - (0)^{2}

STEP 3

Calculate the value of g(0)g(0).
g(0)=6−0=6g(0) =6 -0 =6

STEP 4

Now, substitute g(0)g(0) into the function f(x)f(x).
f(g(0))=f(6)=2(6)+9f(g(0)) = f(6) =2(6) +9

STEP 5

Calculate the value of f(g(0))f(g(0)).
f(g(0))=2()+9=21f(g(0)) =2() +9 =21So, f(g(0))=21f(g(0)) =21.

STEP 6

To find g(f(0))g(f(0)), we first need to find the value of f(0)f(0).
f(0)=2(0)+9f(0) =2(0) +9

STEP 7

Calculate the value of f(0)f(0).
f(0)=2(0)+9=9f(0) =2(0) +9 =9

STEP 8

Now, substitute f(0)f(0) into the function g(x)g(x).
g(f(0))=g()=6−()2g(f(0)) = g() =6 - ()^{2}

STEP 9

Calculate the value of g(f())g(f()).
g(f())=6−(9)2=6−81=−75g(f()) =6 - (9)^{2} =6 -81 = -75So, g(f())=−75g(f()) = -75.

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