#### Didn’t find what you are looking for?

Composite functions

### 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

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

Composite functions

### 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

### 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

### 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

### 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

### 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

### 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

### 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

### 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

### Rewrite the equation so it is slope intercept form. 11x+2y=44

Composite functions

### 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

### 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

### 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

### 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

### 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

### 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

### 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

### 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

...