If g (x) =x 1/x-2 and h(x) = 4 – x, what is the value of (g*h)(-3)?

1 answer:

4 0

G(x) = (x + 1)/(x - 2) and h(x) = 4 - x
(g * h)(x) = (x + 1)(4 - x)/(x - 2)
(g * h)(-3) = (-3 + 1)(4 - (-3))/(-3 - 2) = (-2)(4 + 3)/(-5) = (-2)(7)/(-5) = -14/-5 = 2.8

You might be interested in

Sophia already has 22 plants in her backyard, and she can also grow 2 plants with every seed packet she uses. How many seed pack

Alika [10]

Answer:

Step-by-step explanation:

she already has 22 plants so 2 times 11 = 22 + the 22 she already has

3 0

3 years ago

Solve the differential equation dy dx equals the quotient of x squared and y squared for y = f(x) with the initial condition y(0

Gnoma [55]

$\displaystyle\frac{dy}{dx} = \frac{x^2}{y^2}\ \Rightarrow\ y^2 dy = x^2 dx\ \Rightarrow\ \int y^2 dy = \int x^2 dx\ \Rightarrow\textstyle\ \frac{1}{3}y^3 = \frac{1}{3}x^3 + C. \\ \\
\text{Now } y(0) = 2\ \Rightarrow\ \frac{1}{3}(2)^3 = \frac{1}{3}(0)^3 + C\ \Rightarrow\ \frac{8}{3} = C,\text{ so } \frac{1}{3}y^3 = \frac{1}{3}x^3 + \frac{8}{3}. \\ \\
y^3 = x^3 + 8\ \Rightarrow\ y = \sqrt[3]{x^3 + 8}$

7 0

3 years ago

Fiona has $18 to spend. She spent $4.25, including tax, to buy a notebook. She needs to save $9.75, but she wants to buy a snack

Irina18 [472]

1. $18-4,25=13,75 \\ 13,75-9,75=4 \\ 0,50x \leq 4$ ⇔ $x= \frac{4}{0,50}$ ⇔ $x= 8$
R: She can buy 8 crackers

2. Amy used 13%
Dan used 0,14*100 = 14%
Mike used 0,5*100 = 50%
R: Mike used the greatest amount of milk.

3 0

3 years ago

What is the value of |−25|?

Debora [2.8K]

Answer:

Step-by-step explanation:

3 0

3 years ago

How do I prove that 2 cot 2x = cot x-tan x?

BlackZzzverrR [31]

We will start off working on the right hand side.
cot x - tan x 
= [cos x / sin x] - [sin x / cos x] 
= [(cos x)^ 2 - (sin x)^2] / [sin x cos x] 

This is where it gets a bit tougher if you do not have your formula list with you. 
(cos x)^ 2 - (sin x)^2 = cos(2x) 
sin 2x = 2 sin x cos x 

Note that by arranging the second formula, we will have sin x cos x = (1/2) sin 2x 

Hence, we will get: 
[(cos x)^ 2 - (sin x)^2] / [sin x cos x] 
= [cos 2x] / (1/2)[sin 2x] 
= 2[cos 2x] / [sin 2x] 
= 2cot 2x

7 0

4 years ago