Given f(x) = x^2 + x + 1 h(x) = 3x + 2, evaluate the composite function.

Question

Given f(x) = x^2 + x + 1 h(x) = 3x + 2, evaluate the composite function.

Question

Answers (1)

Relevant Questions

asked 2021-01-08

Given \(\displaystyle{h}{\left({x}\right)}={2}{x}+{4}\) and \(\displaystyle{f{{\left({x}\right)}}}=\frac{{1}}{{2}}{x}+{3}\),
Evaluate the composite function f[h(x)]

See answers (1)

asked 2021-03-06

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

See answers (1)

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

See answers (1)

asked 2021-03-09

Given that
\(\displaystyle{f{{\left({x},{y},{z}\right)}}}={x}{y}+{z},\)
\(\displaystyle{x}={s}^{{2}},\)
\(\displaystyle{y}={s}{t},\)
\(\displaystyle{z}={t}^{{2}},\)
find the composite function.

See answers (1)

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) = ?"

See answers (1)

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))=?

See answers (1)

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

See answers (1)

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 \(\displaystyle{\left({g}\circ{f}\right)}{\left({x}\right)}\)

See answers (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.

See answers (1)

asked 2021-03-05

The number of electric scooters e that a factory can produce per day is a function of the number of hours h it operates and is given by \(\displaystyle{e}{\left({h}\right)}={290}{h},{0}\le{h}\le{10}.\)
The daily cost c to manufacture e electric scooters is given by the function \(\displaystyle{c}{\left({e}\right)}={0.05}{e}^{{2}}+{65}{e}+{1000}.\)
(a) Find \(\displaystyle{\left({c}\circ{e}\right)}{\left({h}\right)}.\)
(b) Evaluate \(\displaystyle{\left({c}\circ{e}\right)}{\left({13}\right)}.\)

See answers (1)

Answer 1

By using the definition of a composite function,
\(\displaystyle{\left({f}\circ{g}\right)}{\left({x}\right)}={f{{\left({h}{\left({x}\right)}\right)}}}\)
\(\displaystyle{\left({f}\circ{g}\right)}{\left({x}\right)}={f{{\left({h}{\left({x}\right)}\right)}}}\)
=f(3x+2)
To find value of f(3x+2) replace x by 3x+2 in function f.
\(\displaystyle{f{{\left({3}{x}+{2}\right)}}}={\left({3}{x}+{2}\right)}^{{2}}+{\left({3}{x}+{2}\right)}+{1}\)
\(\displaystyle={9}{x}^{{2}}+{12}{x}+{4}+{3}{x}+{2}+{1}\)
\(\displaystyle={9}{x}^{{2}}+{15}{x}+{7}\)
Thus, \(\displaystyle{\left({f}\circ{h}\right)}{\left({x}\right)}={9}{x}^{{2}}+{15}{x}+{7}\)
Again by using the definition of a composite function,
\(\displaystyle{\left({h}\circ{f}\right)}{\left({x}\right)}={h}{\left({f{{\left({x}\right)}}}\right)}\)
\(\displaystyle{\left({h}\circ{f}\right)}{\left({x}\right)}={h}{\left({f{{\left({x}\right)}}}\right)}\)
\(\displaystyle={h}{\left({x}^{{2}}+{x}+{1}\right)}\)
To find \(\displaystyle{h}{\left({x}^{{2}}+{x}+{1}\right)}\) replace \(\displaystyle{x}\in{h}{\left({x}\right)}{b}{y}{x}^{{2}}+{x}+{1}\)
\(\displaystyle{h}{\left({x}^{{2}}+{x}+{1}\right)}={3}{\left({x}^{{2}}+{x}+{1}\right)}+{2}\)
\(\displaystyle={3}{x}^{{2}}+{3}{x}+{3}+{2}\)
\(\displaystyle={3}{x}^{{2}}+{3}{x}+{5}\)
Thus, \(\displaystyle{\left({h}\circ{f}\right)}{\left({x}\right)}={3}{x}^{{2}}+{3}{x}+{5}\)

Didn’t find what you are looking for?

Given f(x) = x^2 + x + 1 h(x) = 3x + 2, evaluate the composite function.

Given f(x) = x^2 + x + 1 h(x) = 3x + 2, evaluate the composite function.

Answers (1)

Relevant Questions