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4 years ago

12

Given: f(x)=x^(2)-3 and g(x)=x+1 the composite function g*f is

2 answers:

Ivenika [448]3 years ago

8 0

Answer:

<h2>x³ + x² - 3x - 3</h2>

Step-by-step explanation:

I'm assuming g*f means g times f, so you want to multiply the two functions together.

(x² - 3)(x + 1) Since the product is 2 binomials, use FOIL

= x²(x) + x²(1) - 3(x) - 3(1)

which simplifies to

<h2>x³ + x² - 3x - 3</h2>

qaws [65]3 years ago

4 0

Answer: x³ + x² - 3x - 3

Step-by-step explanation:

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Which glide reflection describes the mapping mc120-2.jpgABC mc120-3.jpg mc120-4.jpgDEF?

sweet-ann [11.9K]

<span>
B. (x,y) (x+2, y-1) and reflected across y=-1</span>

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3 years ago

Find the absolute maximum and absolute minimum values of f on the given interval. f(t) = 2 cos(t) + sin(2t),[0, π/2].

castortr0y [4]

Answer:

The absolute maximum is $\frac{3\sqrt 3}2$ and the absolute minimum value is $0.$

Step-by-step explanation:

Differentiate of $f$ both sides w.r.t. $t$ ,

$f(t)=2 \cos t+\sin 2t$

$\Rightarrow f'(t)=-2\sin t+2\cos 2t$

Now take $f'(t)=0$

$\Rightarrow -2\sin t+2\cos 2t=0$

$\Rightarrow 2\cos 2t=2\sin t$

$\Rightarrow \cos 2t=\sin t$

$\Rightarrow 1-2\sin ^2t =\sin t \quad \quad [\because \cos 2t = 1-2\sin ^2t]$

$\Rightarrow 2\sin ^2t+\sin t-1=0$

$\Rightarrow 2\sin ^2t+2\sin t-\sin t-1=0$

$\Rightarrow 2\sin t(\sin t+1)-1(\sin t+1)=0$

$\Rightarrow (\sin t+1)(2\sin t-1)=0$

$\Rightarrow \sin t+1=0 \;\text{and}\; 2\sin t-1=0$

$\Rightarrow \sin t =-1 \;\text{and}\; \sin t =\frac 12$

In the interval $0\leq t\leq \frac {\pi}2$ , the answer to this problem is $\frac {\pi}6$

Now find the second derivative of $f(t)$ w.r.t. $t$ ,

$f''(t)=-2\cos t-4\sin 2t$

$\Rightarrow \left[f''(t)\right]_{t=\frac {\pi}6}=-2\times \frac {\sqrt 3}2-4\times \frac{\sqrt 3}2=-3\sqrt 3$

Thus, $f(t)$ is maximum at $t=\frac {\pi}6$ and minimum at $t=0$

$\left[f(t)\right]_{t=\frac {\pi}6}=2\times \frac {\sqrt 3}2+\frac{\sqrt 3}2=\frac{3\sqrt 3}2\;\text{and}\;\left[f(t)\right]_{t=\frac{\pi}2}= 2\times 0+0=0$

Hence, the absolute maximum is $\frac{3\sqrt 3}2$ and the absolute minimum value is $0$ .

7 0

3 years ago

Two parrelel chords 16 centimeters and 30 centimeters long are 23 centimeters apart. find the length of the radius of the circle

BARSIC [14]

<span>r^2 = 529 - 46x + x^2 + 64
r^2 = x^2 - 46x + 593
replace r^2 with (x^2+ 225)
x^2 + 225 = x^2 - 46x + 593
x^2 - x^2 + 46x = 593 - 225
46x = 368
x = 368/46
x = 8 cm
Find the radius
r^2 = 8^2 + 225
r^2 = 289
r =

r = 17 cm is the radius</span>

7 0

3 years ago

In what direction and by how many units is the graph of f(x) = −3 cos(2x − π) + 2 vertically and horizontally shifted

MakcuM [25]

Answer:

Vertical shift is 2 units top and horizontal shift is $\frac{\pi }{2}$ units to the right

Step-by-step explanation:

Consider the function f(x) = a cos(bx + c) + d.

In this graph, the horizontal shift is -c/b and the vertical shift is d.

Let's compare our graph, f(x) = -3 cos(2x - π) + 2 with this graph.

Here, a = -3, b = 2, c = -π and d = 2.

So, vertical shift = d = 2 units top and

horizontal shift = $-\frac{c}{b} =-\frac{-\pi }{2} =\frac{\pi}{2}$ units to the right.

8 0

3 years ago

A city bus driver says the number of miles to gallons of gas for his bus can be represented by the ratio 12 : 4. How many miles

sergey [27]

Answer:

The bus can travel 3 miles with 1 gallon of gas

Step-by-step explanation:

Hope this helps!

4 0

3 years ago