For the following problems, find the function f ° g and the domain of f ° g .

1 answer:

5 0

$2)\\f(x)=\dfrac{x}{x+4}\\\\g(x)=\dfrac{16}{x+2}\\\\Domain:\\\\D_f:x\neq-4\\\\D_g:x\neq-2\\\\(f\ \circ\ g)(x)=\dfrac{\frac{x}{x+4}}{\frac{16}{x+2}}=\dfrac{x}{x+4}\cdot\dfrac{x+2}{16}=\dfrac{x^2+2x}{16x+64}\\\\Domain:\\\\16x+64\neq0\to16x\neq-64\to\boxed{x\neq-4}$

$3)\\f(x)=\sqrt{x}\\\\g(x)=5x+5\\\\Domain:\\\\D_f:x\geq0\\\\D_g:x\in\mathbb{R}\\\\(f\ \circ\ g)(x)=\sqrt{5x+5}\\\\Domain:\\\\5x+5\geq0\to5x\geq-5\to\boxed{x\geq-1}$

You might be interested in

You manage a coffee shop. you begin the day with 25 pounds of coffee beans. you use 4 pounds of beans to brew coffee and sell 20

Dennis_Churaev [7]

So we started with 25, then after we lost a solid 4 as a given variable. So now we have 21 beans. Later we find that 6 pounds are left and are in not part of the beans sold that can be effectively used to find the weight of each equal bean bag. So we subtract 6 from 21. We get 15 pounds that were sold in 20 bags. The equation to find the weight of each bag from there is :

15 lb/10 bags

From there it equals 0.75 lb per bag.

7 0

3 years ago

the revenue for the school play is given by: r=-50t^2 + 300t, where “t” is ticket price in dollars. The cost to produce the play

artcher [175]

ANSWER

EXPLANATION

The revenue function is

$r = - 50 {t}^{2} + 300t$