Given f(x) = x^2, g(x) = x + 7 Find (f @ g)(x). Find the domain of (f @ g)(x). Find (g @ f)(x). Find the domain of (g @ f)(x). Find (f @ f)(x). Find the domain of (f @ f)(x). Find (g @ g)(x). Find the domain of (g @ g)(x).

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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?
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asked 2021-02-25

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asked 2020-11-26

Given
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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,
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asked 2020-11-24

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asked 2021-01-10

Compose the following function and state the domain of the composed function.
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asked 2021-02-25

Find and simplify in expression for the idicated composite functions. State the domain using interval notation.
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asked 2021-03-05

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asked 2021-02-24

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asked 2020-12-25

Let f(x) = \(\displaystyle{4}{x}^{{2}}–{6}\) and \(\displaystyle{g{{\left({x}\right)}}}={x}–{2}.\)
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(b) Find \(\displaystyle{\left({f}\circ{g}\right)}{\left(−{1}\right)}\). Show work.

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Answer 1

\(\displaystyle{f}\circ{g{{\left({x}\right)}}}={f{{\left({g{{\left({x}\right)}}}\right)}}}={\left({g{{\left({x}\right)}}}\right)}^{{2}}={\left({x}+{7}\right)}^{{2}}\)
\(\displaystyle={x}^{{2}}+{14}{x}+{49}\)
It is a polunomial so domain is all real numbers
Domain of \(\displaystyle{f}\circ{g{{\left({x}\right)}}}\) is \(\displaystyle{\left(-\infty,\infty\right)}\)
\(\displaystyle{g}\circ{f{{\left({x}\right)}}}={f{{\left({x}\right)}}}+{7}={x}^{{2}}+{7}\)
It is a polunomial so domain is all real numbers
Domain of \(\displaystyle{g}\circ{f{{\left({x}\right)}}}\) is \(\displaystyle{\left(-\infty,\infty\right)}\)
\(\displaystyle{f}\circ{f{{\left({x}\right)}}}={\left({f{{\left({x}\right)}}}\right)}^{{2}}={\left({x}^{{2}}\right)}^{{2}}={x}^{{4}}\)
It is a polunomial so domain is all real numbers
Domain of \(\displaystyle{f}\circ{f{{\left({x}\right)}}}\) is \(\displaystyle{\left(-\infty,\infty\right)}\)
\(\displaystyle{g}\circ{g{{\left({x}\right)}}}={g{{\left({x}\right)}}}+{7}={x}+{7}+{7}={x}+{14}\)
It is a polunomial so domain is all real numbers
Domain of \(\displaystyle{g}\circ{g{{\left({x}\right)}}}\) is \(\displaystyle{\left(-\infty,\infty\right)}\)

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Given f(x) = x^2, g(x) = x + 7 Find (f @ g)(x). Find the domain of (f @ g)(x). Find (g @ f)(x). Find the domain of (g @ f)(x). Find (f @ f)(x). Find the domain of (f @ f)(x). Find (g @ g)(x). Find the domain of (g @ g)(x).

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