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

Question
Composite functions
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 $$\displaystyle{g}∘{f}$$

2021-01-16
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:
PSK(f o g)(x)=f(g(x)) =(4x^2-3x-9)-3 =4x^2-3x-12ZSK
To find g o f, replace x of g by f(x) and simplify:
PSK(g o 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+36ZSK

### Relevant Questions

Let f(x) = $$\displaystyle{4}{x}^{{2}}–{6}$$ and $$\displaystyle{g{{\left({x}\right)}}}={x}–{2}.$$
(a) Find the composite function $$\displaystyle{\left({f}\circ{g}\right)}{\left({x}\right)}$$ and simplify. Show work.
(b) Find $$\displaystyle{\left({f}\circ{g}\right)}{\left(−{1}\right)}$$. Show work.
Find the composite functions $$\displaystyle{f}\circ{g}$$ and $$\displaystyle{g}\circ{f}$$. Find the domain of each composite function. Are the two composite functions equal?
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a. Describe what the functions f and g model in terms of the price of the computer.
b. Find $$\displaystyle{\left({f}\circ{g}\right)}{\left({x}\right)}$$ and describe what this models in terms of the price of the computer.
c. Repeat part (b) for $$\displaystyle{\left({g}\circ{f}\right)}{\left({x}\right)}$$.
d. Which composite function models the greater discount on the computer, $$\displaystyle{f}\circ{g}$$ or $$\displaystyle{g}\circ{f}$$?
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Given f(x) = 5x − 5 and g(x) = 5x − 1,
Evaluate the composite function g[f(0)]
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$$\displaystyle{f{{\left({x}\right)}}}={71}{e}^{{{0.2}{x}}}$$
{g(h), h(x)} = ?
f'(x) = ?"
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$$\displaystyle{f{{\left({x}\right)}}}={3}{x}-{1}$$
$$\displaystyle{g{{\left({x}\right)}}}=\frac{{1}}{{{x}+{3}}}$$
Find $$\displaystyle{\left({g}\circ{f}\right)}{\left({x}\right)}$$
Decide whether the composite functions, $$\displaystyle{f}\circ{g}$$ and $$\displaystyle{g}\circ{f}$$, are equal to x.
$$\displaystyle{f{{\left({x}\right)}}}={x}^{{3}}+{9}$$
$$\displaystyle{g{{\left({x}\right)}}}={\sqrt[{{3}}]{{{x}-{9}}}}$$
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$$\displaystyle{z}={t}^{{2}},$$
Given $$\displaystyle{h}{\left({x}\right)}={2}{x}+{4}$$ and $$\displaystyle{f{{\left({x}\right)}}}=\frac{{1}}{{2}}{x}+{3}$$,