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SECONDARY
CALCULUS AND ANALYSIS
PRECALCULUS
COMPOSITE FUNCTIONS
Secondary
Calculus and Analysis
Precalculus
Matrices
Polynomials
Probability and combinatorics
Composite functions
Vectors
Trigonometry
Complex numbers
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Polynomial graphs
Transformations of functions
Calculus 1
Calculus 2
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Statistics and Probability
Math Word Problem
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Composite functions Answers
Composite functions
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.
Composite functions
asked 2021-03-06
Given f(x) = 5x − 5 and g(x) = 5x − 1,
Evaluate the composite function g[f(0)]
Composite functions
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
\(\displaystyle{\left({c}\circ{e}\right)}{\left({13}\right)}.\)
Composite functions
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))=?
Composite functions
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
\(\displaystyle{\left({g}\circ{f}\right)}{\left({x}\right)}\)
Composite functions
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
Composite functions
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)
Composite functions
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) = ?"
Composite functions
asked 2021-02-01
Suppose that the dunctions q and r are defined as follows.
\(\displaystyle{q}{\left({x}\right)}={x}^{{2}}+{5}\)
\(\displaystyle{r}{\left({x}\right)}=\sqrt{{{x}+{3}}}\)
Find the following.
\(\displaystyle{q}\circ{r}{\left({1}\right)}=?\)
\(\displaystyle{\left({r}\circ{q}\right)}{\left({1}\right)}=?\)
Composite functions
asked 2021-01-31
Cameron stops to get gas soon after beginning a road trip. He checks his distance from home 2 hours after filling his gas tank and checks again 3 hours later. The first time he checked, he was 170 miles from home. The second time, he was 365 miles from home. What equation models Cameron's distance from home as a function of the time since getting gas?
Composite functions
asked 2021-01-27
Rewrite the equation so it is slope intercept form. 11x+2y=44
Composite functions
asked 2021-01-25
Let
\(\displaystyle{f{{\left({x}\right)}}}={4}{x}+{2}\)
and
\(\displaystyle{g{{\left({x}\right)}}}={3}{x}^{{2}}+{3}{x}\)
.
After simplifying,
\(\displaystyle{\left({f}\circ{g}\right)}{\left({x}\right)}=?\)
Composite functions
asked 2021-01-16
A car dealership offers a $1300 rebate and a 15% discount off the price of a new car. Let p be the sticker price of a new car on the dealer's lot, r the price after the rebate, and d the discounted price. Then r(p) = p − 1300 and d(p) = 0.85p.
a) Write a composite function for the dealer taking the rebate first and then the discount.
d[r(p)] =
b) Write a composite function for the dealer taking the discount first and then the rebate.
r[d(p)] =
Composite functions
asked 2021-01-15
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
\(\displaystyle{g}∘{f}\)
Composite functions
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)
\(\displaystyle{g{{\left({f{{\left(-{2}\right)}}}\right)}}}\)
Composite functions
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)]
Composite functions
asked 2021-01-05
Suppose that the dunctions q and r are defined as follows.
\(\displaystyle{q}{\left({x}\right)}={x}^{{2}}+{7}\)
r(x)=sqrt(x+8)ZSK
Find the following.
\(\displaystyle{q}\circ{r}{\left({1}\right)}=?\)
\(\displaystyle{\left({r}\circ{q}\right)}{\left({1}\right)}=?\)
Composite functions
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.
Composite functions
asked 2020-12-24
Let
\(\displaystyle{f{{\left({x}\right)}}}={x}^{{2}}+{9}{x}\)
and
\(\displaystyle{g{{\left({x}\right)}}}={9}{x}+{8}\)
perform the composition or operation indicated below
\(\displaystyle{\left({f}\circ{g}\right)}{\left({5}\right)}\)
simplify the answer
Composite functions
asked 2020-11-29
How can the composite function be evaluated?
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