f(x)=x−3 and g(x)=4x2−3x−9g(x)=4x^2−3x−9. Find composite function f∘g and g∘f

Composite functions
asked 2021-01-15

f(x)=x−3 and \(\displaystyle{g{{\left({x}\right)}}}={4}{x}{2}−{3}{x}−{9}{g{{\left({x}\right)}}}={4}{x}^{{2}}−{3}{x}−{9}\). Find composite function \(\displaystyle{f}∘{g}\) and \(\displaystyle{g}∘{f}\)

Answers (1)


We are given: f(x)=x-3 and g(x) = \(\displaystyle{4}{x}^{{2}}-{3}{x}-{9}\)
To find f o g replace x of x by g(x) and simplify:
\((f ∘ g)(x)=f(g(x)) =(4x^2-3x-9)-3 =4x^2-3x-12\)
To find g o f, replace x of g by f(x) and simplify:
\((g ∘ f)(x)=g(f(x)) =4((x-3)^2)-3(x-3)-9 =4(x^2-6x+9)-3(x-3)-9 =4x^2-24x+36-3x+9-9 =4x^2-27x+36\)

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