Ask question

# Find the composite functions f @ g and g @ f. Find the domain of each composite function. Are the two composite functions equal? f(x) = x^2 − 1 g(x) = −x # Find the composite functions f @ g and g @ f. Find the domain of each composite function. Are the two composite functions equal? f(x) = x^2 − 1 g(x) = −x

Question
Composite functions asked 2020-10-18
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?
$$\displaystyle{f{{\left({x}\right)}}}={x}^{{2}}−{1}$$
g(x) = −x

## Answers (1) 2020-10-19
To find the composite function, $$\displaystyle{f}\circ{g}$$ and $$\displaystyle{g}\circ{f}$$ and also their respective domains.
Solution:
The functions are $$\displaystyle{f{{\left({x}\right)}}}={x}^{{2}}−{1}$$ and g(x)=−x.ZSK
The function $$\displaystyle{f}\circ{g}$$ can be evaluated as,
$$\displaystyle{f}\circ{g}={f{{\left({g{{\left({x}\right)}}}\right)}}}$$
$$\displaystyle={f{{\left(−{x}\right)}}}$$
$$\displaystyle={\left(−{x}\right)}^{{2}}−{1}$$
$$\displaystyle={x}^{{2}}−{1}$$
The function $$\displaystyle{g}\circ{f}$$ can be evaluated as,
$$\displaystyle{g}\circ{f}={g{{\left({f{{\left({x}\right)}}}\right)}}}$$
$$\displaystyle={g{{\left({x}^{{2}}−{1}\right)}}}$$
$$\displaystyle=−{\left({x}^{{2}}−{1}\right)}$$
$$\displaystyle=−{x}^{{2}}+{1}$$
The obtained composite function are not equal. And the domain for both the function is complete real numbers as it is defined for each value of x.

### Relevant Questions asked 2021-02-25
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
f(x) = 3x + 1
g(x) = −x asked 2020-11-08
The regular price of a computer is x dollars. Let f(x) = x - 400 and g(x) = 0.75x. Solve,
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 $$\displaystyle{g}\circ{f}$$? asked 2021-02-25
Find and simplify in expression for the idicated composite functions. State the domain using interval notation.
$$\displaystyle{f{{\left({x}\right)}}}={3}{x}-{1}$$
$$\displaystyle{g{{\left({x}\right)}}}=\frac{{1}}{{{x}+{3}}}$$
Find $$\displaystyle{\left({g}\circ{f}\right)}{\left({x}\right)}$$ asked 2020-10-27
Decide whether the composite functions, $$\displaystyle{f}\circ{g}$$ and $$\displaystyle{g}\circ{f}$$, are equal to x.
$$\displaystyle{f{{\left({x}\right)}}}={x}^{{3}}+{9}$$
$$\displaystyle{g{{\left({x}\right)}}}={\sqrt[{{3}}]{{{x}-{9}}}}$$ asked 2021-03-06
Given f(x) = 5x − 5 and g(x) = 5x − 1,
Evaluate the composite function g[f(0)] asked 2020-10-21
Given
$$\displaystyle{f{{\left({x}\right)}}}={x}^{{2}},{g{{\left({x}\right)}}}={x}+{7}$$
Find $$\displaystyle{\left({f}\circ{g}\right)}{\left({x}\right)}.$$
Find the domain of $$\displaystyle{\left({f}\circ{g}\right)}{\left({x}\right)}.$$
Find $$\displaystyle{\left({g}\circ{f}\right)}{\left({x}\right)}.$$
Find the domain of $$\displaystyle{\left({g}\circ{f}\right)}{\left({x}\right)}.$$
Find $$\displaystyle{\left({f}\circ{f}\right)}{\left({x}\right)}.$$
Find the domain of $$\displaystyle{\left({f}\circ{f}\right)}{\left({x}\right)}.$$
Find $$\displaystyle{\left({g}\circ{g}\right)}{\left({x}\right)}.$$
Find the domain of $$\displaystyle{\left({g}\circ{g}\right)}{\left({x}\right)}.$$ asked 2020-11-26
Given
$$\displaystyle{f{{\left({x}\right)}}}={2}-{x}{2},{g{{\left({x}\right)}}}=\sqrt{{{x}+{2}}}$$
$$\displaystyle{f{{\left({x}\right)}}}=\sqrt{{{x}}},{g{{\left({x}\right)}}}=\sqrt{{{1}-{x}}}$$
(a) write formulas for $$\displaystyle{f}\circ{g}$$ and $$\displaystyle{g}\circ{f}$$ and find the
(b) domain and
(c) range of each. asked 2021-02-26
Rewrite the given pair of functions as one composite form
$$\displaystyle{g{{\left({x}\right)}}}=\sqrt{{{5}{x}^{{2}}}}$$
$$\displaystyle{x}{\left({w}\right)}={2}{e}^{{w}}$$
g(x(ww))=?
Evalute the composite function at 1.
g(x(1))=? asked 2020-12-25
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. asked 2021-01-10
Compose the following function and state the domain of the composed function.
$$\displaystyle{f{{\left({x}\right)}}}=\frac{{1}}{{x}}-{1}$$
$$\displaystyle{g{{\left({x}\right)}}}=\sqrt{{{1}-{x}^{{2}}}}$$
a) $$\displaystyle{g{{\left({f{{\left(-{2}\right)}}}\right)}}}$$
...