All categories

3 years ago

Let f(x) = 2x, g(x) = x2 + 2, and h(x) = -4x + 3. Find the composite function.

Mathematics

1 answer:

Margarita [4]3 years ago

3 0

$(g\circ f)(x)=g(f(x))\\\\
(g\circ f)(x)=(2x)^2+2=4x^2+2 \Rightarrow B$

You might be interested in

A hotel has $504 to buy new pillows. If the cost of each pillow is $6, how many pillows will the hotel be able to buy? A) 78 B)

Naddik [55]

Hello there!
You can use the equation:
504 ÷ 6
84
The hotel can buy 84 pillows.
Hope this helped! :D

4 0

2 years ago

Read 2 more answers

The temperature on a winter night is 8 Fahrenheit. The temperature decreases by 14 Fahrenheit. What is the new temperature, in d

-BARSIC- [3]

Answer: -6 (8-14=-6)

Step-by-step explanation:

8-14 = -6

7 0

3 years ago

You , malakhi , yanis , nyla , Aaliyah go to a new tapas restaurant in jamaica , queens each of you order 6 small dishes that ea

BlackZzzverrR [31]

each dish costs two dollars.

3 0

2 years ago

PLZZZ HELP MEEEE

Naddika [18.5K]

Answer:

in 19 81 has in crimn that day there are a war

6 0

2 years ago

Read 2 more answers

Find the absolute extrema for f(x,y)=4-x^2-y^4+1/2y^2 over the closed disk D:x^2+y^2 is less than or equal to 1

algol [13]

Find the critical points of $f(x,y)$ :

$\dfrac{\partial f}{\partial x}=-2x=0\implies x=0$

$\dfrac{\partial f}{\partial y}=y-4y^3=y(1-4y^2)=0\implies y=0\text{ or }y=\pm\dfrac12$

All three points lie within $D$ , and $f$ takes on values of

$\begin{cases}f(0,0)=4\\f\left(0,-\frac12\right)=\frac{65}{16}\\f\left(0,\frac12\right)=\frac{65}{16}\end{cases}$

Now check for extrema on the boundary of $D$ . Convert to polar coordinates:

$f(x,y)=f(\cos t,\sin t)=g(t)=4-\cos^2-\sin^4t+\dfrac12\sin^2t=3+\dfrac32\sin^2t-\sin^4t$

Find the critical points of $g(t)$ :

$\dfrac{\mathrm dg}{\mathrm dt}=3\sin t\cos t-4\sin^3t\cos t=\sin t\cos t(3-4\sin^2t)=0$

$\implies\sin t=0\text{ or }\cos t=0\text{ or }\sin t=\pm\dfrac{\sqrt3}2$

$\implies t=n\pi\text{ or }t=\dfrac{(2n+1)\pi}2\text{ or }\pm\dfrac\pi3+2n\pi$

where $n$ is any integer. There are some redundant critical points, so we'll just consider $0\le t< 2\pi$ , which gives

$t=0\text{ or }t=\dfrac\pi3\text{ or }t=\dfrac\pi2\text{ or }t=\pi\text{ or }t=\dfrac{3\pi}2\text{ or }t=\dfrac{5\pi}3$

which gives values of

$\begin{cases}g(0)=3\\g\left(\frac\pi3\right)=\frac{57}{16}\\g\left(\frac\pi2\right)=\frac72\\g(\pi)=3\\g\left(\frac{3\pi}2\right)=\frac72\\g\left(\frac{5\pi}3\right)=\frac{57}{16}\end{cases}$

So altogether, $f(x,y)$ has an absolute maximum of 65/16 at the points (0, -1/2) and (0, 1/2), and an absolute minimum of 3 at (-1, 0).

5 0

2 years ago