# Rewrite the given pair of functions as one composite form g(x)=sqrt(5x^2) x(w)=2e^w g(x(ww))=? Evalute the composite function at 1. g(x(1))=?

Question
Composite functions
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))=?

2021-02-27
Rewrite the given pair as one composite function as follows.
$$\displaystyle{g{{\left({x}{\left({w}\right)}\right)}}}={g{{\left({2}{e}^{{w}}\right)}}}=\sqrt{{{5}\cdot{\left({2}{e}^{{2}}\right)}^{{2}}}}$$
Evaluate the above composite function at 1
$$\displaystyle{g{{\left({x}{\left({1}\right)}\right)}}}=\sqrt{{{5}{\left({2}{e}^{{1}}\right)}^{{2}}}}=\sqrt{{{5}{\left({2}{e}\right)}^{{2}}}}=\sqrt{{{5}\cdot{4}\cdot{e}^{{2}}}}={2}\sqrt{{{5}}}{e}\approx{12.16}$$

### Relevant Questions

Given f(x) = 5x − 5 and g(x) = 5x − 1,
Evaluate the composite function g[f(0)]
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
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
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 $$\displaystyle{g}\circ{f}$$?
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) = ?"
consider the product of 3 functions $$\displaystyle{w}={f}\times{g}\times{h}$$. Find an expression for the derivative of the product in terms of the three given functions and their derivatives. (Remeber that the product of three numbers can be thought of as the product of two of them with the third
$$\displaystyle{w}'=$$?
Given
$$\displaystyle{f{{\left({x}\right)}}}={x}^{{2}}+{x}+{1}$$
h(x) = 3x + 2,
evaluate the composite function.
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 $$\displaystyle{\left({g}\circ{f}\right)}{\left({x}\right)}$$
$$\text{quotient}+\frac{remainder}{divisor}$$
$$\displaystyle{f{{\left({x}\right)}}}={\frac{{{1}}}{{{x}}}}$$
$$\displaystyle{g{{\left({x}\right)}}}={\frac{{{2}{x}+{7}}}{{{x}+{3}}}}$$
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.