Find and simplify in expression for the idicated composite functions. State the domain using interval notation. f(x)=3x-1 g(x)=1/(x+3) Find ([email protected])(x)

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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

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asked 2020-10-27

Decide whether the composite functions, \(\displaystyle{f}\circ{g}\) and \(\displaystyle{g}\circ{f}\), are equal to x.
\(\displaystyle{f{{\left({x}\right)}}}={x}^{{3}}+{9}\)
\(\displaystyle{g{{\left({x}\right)}}}={\sqrt[{{3}}]{{{x}-{9}}}}\)

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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

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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.

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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 \(\displaystyle{g}\circ{f}\)?

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asked 2021-02-24

For f(x)=6/x and g(x)=6/x, find the following functions. a) ([email protected])(x) b) ([email protected])(x) c) ([email protected])(7) d) ([email protected])(7)

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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.

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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) \(\displaystyle{g{{\left({f{{\left(-{2}\right)}}}\right)}}}\)

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asked 2021-02-06

For the composite function, identify an inside function and an oposite fnction abd write the derivative with respect to x of the composite function. (The function is of the form f(x)=g(h(x)). Use non-identity dunctions for g(h) and h(x).)
\(\displaystyle{f{{\left({x}\right)}}}={71}{e}^{{{0.2}{x}}}\)
{g(h), h(x)} = ?
f'(x) = ?"

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asked 2021-03-06

Given f(x) = 5x − 5 and g(x) = 5x − 1,
Evaluate the composite function g[f(0)]

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Answer 1

Obtain the composite function, \(\displaystyle{g}\circ{f{{\left({x}\right)}}}\)
\(\displaystyle{g}\circ{f{{\left({X}\right)}}}={g{{\left({f{{\left({x}\right)}}}\right)}}}\)
\(\displaystyle=\frac{{1}}{{{\left({f{{\left({x}\right)}}}\right)}+{3}}}\)
\(\displaystyle=\frac{{1}}{{{\left({3}{x}-{1}\right)}+{3}}}\)
\(\displaystyle=\frac{{1}}{{{3}{x}+{2}}},{x}\ne-\frac{{2}}{{3}}\)
Here, the simplified expression for the composite function is
\(\displaystyle{g}\circ{f{{\left({x}\right)}}}=\frac{{1}}{{{3}{x}+{2}}},{x}\ne-\frac{{2}}{{3}}\)
The composite function defined for all values of x except at \(\displaystyle{x}=-\frac{{2}}{{3}}\) that is defined all values on the left and right of \(\displaystyle{x}=-\frac{{2}}{{3}}\) but not at \(\displaystyle{x}=-\frac{{2}}{{3}}\), thus the domain in the interval notation becomes \(\displaystyle{\left(-\infty,-\frac{{2}}{{3}}\right)}\cup{\left(\frac{{2}}{{3}},\infty\right)}\)

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Find and simplify in expression for the idicated composite functions. State the domain using interval notation. f(x)=3x-1 g(x)=1/(x+3) Find ([email protected])(x)

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