Let f(x) = 4x^2–6 and g(x)=x–2. (a) Find the composite function ([email protected])(x) and simplify. Show work. (b) Find ([email protected])(−1). Show work.

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Let f(x) = 4x^2–6 and g(x)=x–2. (a) Find the composite function ([email protected])(x) and simplify. Show work. (b) Find ([email protected])(−1). Show work.

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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

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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 2021-01-25

Let \(\displaystyle{f{{\left({x}\right)}}}={4}{x}+{2}\) and \(\displaystyle{g{{\left({x}\right)}}}={3}{x}^{{2}}+{3}{x}\).
After simplifying, \(\displaystyle{\left({f}\circ{g}\right)}{\left({x}\right)}=?\)

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asked 2021-05-16

Consider the curves in the first quadrant that have equationsy=Aexp(7x), where A is a positive constant. Different valuesof A give different curves. The curves form a family,F. Let P=(6,6). Let C be the number of the family Fthat goes through P.
A. Let y=f(x) be the equation of C. Find f(x).
B. Find the slope at P of the tangent to C.
C. A curve D is a perpendicular to C at P. What is the slope of thetangent to D at the point P?
D. Give a formula g(y) for the slope at (x,y) of the member of Fthat goes through (x,y). The formula should not involve A orx.
E. A curve which at each of its points is perpendicular to themember of the family F that goes through that point is called anorthogonal trajectory of F. Each orthogonal trajectory to Fsatisfies the differential equation dy/dx = -1/g(y), where g(y) isthe answer to part D.
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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 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 \(\displaystyle{g}∘{f}\)

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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 2020-11-26

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 2020-11-24

Find the domain of the coposite function [email protected]

\(\displaystyle{f{{\left({x}\right)}}}=\frac{{5}}{{{x}+{9}}}\)
g(x)=x+6

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

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Answer 1

(a) The composite function is,
\(\displaystyle{\left({f}\circ{g}\right)}{\left({x}\right)}={f{{\left({g{{\left({x}\right)}}}\right)}}}\)
\(\displaystyle={f{{\left({x}-{2}\right)}}}\)
\(\displaystyle={4}{\left({x}-{2}\right)}^{{2}}-{6}\) [replacing x by x-2 in f(x)]
\(\displaystyle={4}{\left({x}^{{2}}-{4}{x}+{4}\right)}-{6}\)
\(\displaystyle={4}{x}^{{2}}-{16}{x}+{16}-{6}\)
\(\displaystyle{4}{x}^{{2}}-{16}{x}+{10}\)
b) Replacing x by -1 in the composite function, we get
\(\displaystyle{\left({f}\circ{g}\right)}{\left(-{1}\right)}={4}{\left(-{1}\right)}^{{2}}-{16}{\left(-{1}\right)}+{10}\)
=4+16+10
=30

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Let f(x) = 4x^2–6 and g(x)=x–2. (a) Find the composite function ([email protected])(x) and simplify. Show work. (b) Find ([email protected])(−1). Show work.

Let f(x) = 4x^2–6 and g(x)=x–2. (a) Find the composite function ([email protected])(x) and simplify. Show work. (b) Find ([email protected])(−1). Show work.

Answers (1)

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