Given f(x) = x^2 + x + 1 h(x) = 3x + 2, evaluate the composite function.

Rui Baldwin 2020-11-01 Answered
Given
f(x)=x2+x+1
h(x) = 3x + 2,
evaluate the composite function.
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Expert Answer

Nicole Conner
Answered 2020-11-02 Author has 97 answers
By using the definition of a composite function,
(fg)(x)=f(h(x))
(fg)(x)=f(h(x))
=f(3x+2)
To find value of f(3x+2) replace x by 3x+2 in function f.
f(3x+2)=(3x+2)2+(3x+2)+1
=9x2+12x+4+3x+2+1
=9x2+15x+7
Thus, (fh)(x)=9x2+15x+7
Again by using the definition of a composite function,
(hf)(x)=h(f(x))
(hf)(x)=h(f(x))
=h(x2+x+1)
To find h(x2+x+1) replace xh(x)byx2+x+1
h(x2+x+1)=3(x2+x+1)+2
=3x2+3x+3+2
=3x2+3x+5
Thus, (hf)(x)=3x2+3x+5
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