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3 years ago

If f(x)= x^2-1 and g(x)=2x-3, what is the domain of (fog)(x)

Mathematics

1 answer:

My name is Ann [436]3 years ago

5 0

Answer:

$\large\boxed{\text{The domain is the set of all real numbes}\to x\in\mathbb{R}}$

Step-by-step explanation:

$f(x)=x^2-1,\ g(x)=2x-3\\\\(f\circ g)(x)-\text{instead of x in the function equation f(x) put}\ 2x-3:\\\\(f\circ g)(x)=(2x-3)^2-1\qquad\text{use}\ (a-b)^2=a^2-2ab+b^2\\\\(f\circ g)(x)=(2x)^2-2(2x)(3)+3^2-1=4x^2-12x+9-1\\\\(f\circ g)(x)=4x^2-12x+8\\\\\text{the domain is the set of all real numbes}\to x\in\mathbb{R}$

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Is 11.5 rational or irrational

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11.5 is a rational number

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3 years ago

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A bus travels with a constant speed of 48 miles per hour. How long will it take to travel 60 miles? Write your answer as a decim

agasfer [191]

Answer:

1.25 hours, I think?

Step-by-step explanation:

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Leo wants to paint a mural that covers a wall with an area of 300 square feet. The height of the wall is 1/3 of its length. What

andrew-mc [135]

Answer:

Length = 30

Height = 10

Step-by-step explanation:

Formula for the area = height * length. We know that the height of the wall is 1/3 of its length. This gives us another formula which is $h=\frac{1}{3} l$

Now substitute this into the formula, while knowing that the area is 300.

So we have 300 = $\frac{1}{3}l * l$

Solving for l gives us 30 and then substituting it back into the equation

$h = \frac{1}{3} l$ , will give us that the height is 10.

Hope this helps

4 0

3 years ago

Pls help me<br>I m giving brainliest <br>

navik [9.2K]

Step-by-step explanation:

the general line equation format is

y = ax + b

a is the slope or gradient of the line. it is the ratio of "y coordinate change / x coordinate change".

b is the y-intercept, the y value when x = 0. we get this by putting one point into the equation and solve for b.

(i)

A (3, 5)

B (5, 9)

x changes by +2 (from 3 to 5).

y changes by +4 (from 5 to 9).

so, the slope (or gradient) is +4/+2 = 2

(ii)

the semi-finished equation is

y = 2x + b

let's use A to get b :

5 = 2×3 + b = 6 + b

b = -1

and the full equation is

y = 2x - 1

(iii)

for point (4, k) we get

k = 2×4 - 1 = 8 - 1 = 7

3 0

2 years ago

What is (f*g)(x)? f(x)=x^4-9, g(x)=x^3+9

sladkih [1.3K]

(x^4 - 9)(x^3 + 9)
This is a binomial * binomial. Use the FOIL method for multiplying.
First, outer, inner, last.
x^4 * x^3 = x^7
x°^4 * 9 = 9x^4
-9 * x^3 = -9 x^3
-9 * 9 = -81
Putting it back together.
x^7 +9x^4 -9x^3 - 81

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2 years ago