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3 years ago

8

Use the functions f(x) = 4x − 5 and g(x) = 3x + 9 to complete the function operations listed below.

1 answer:

JulijaS [17]3 years ago

6 0

A:

(f+g)(x)=f(x)+g(x)

(f+g)(x)=4x-5+3x+9

(f+g)(x)=7x+4

B:

(f•g)(x)=f(x)•g(x)

(f•g)(x)=(4x-5)(3x+9)

(f•g)(x)=12x^2-15x+36x-45

(f•g)(x)=12x^2+21x-45

C:

(f○g)(x)=f(g(x))

(f○g)(x)=4(3x+9)-5

(f○g)(x)=12x+36-5

(f○g)(x)=12x+31

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Read 2 more answers

What is an equation of the line that passes through the point ( 6 , − 2 ) (6,−2) and is perpendicular to the line 6 x + y = 2 6x

Diano4ka-milaya [45]

Answer:

An equation of the line that passes through the point (6, − 2) and is perpendicular to the line will be:

$y=\frac{1}{6}x-3$

Step-by-step explanation:

We know that the slope-intercept form of the line equation is

y=mx+b

where m is the slope and b is the y-intercept.

Given the line

6x+y=2

Simplifying the equation to write into the slope-intercept form

y = -6x+2

So, the slope = -6

As we know that the slope of the perpendicular line is basically the negative reciprocal of the slope of the line.

Thus, the slope of the perpendicular line will be: -1/-6 = 1/6

Therefore, an equation of the line that passes through the point (6, − 2) and is perpendicular to the line will be

$y-y_1=m\left(x-x_1\right)$

substituting the values m = 1/6 and the point (6, -2)

$y-\left(-2\right)=\frac{1}{6}\left(x-6\right)$

$y+2=\frac{1}{6}\left(x-6\right)$

subtract 2 from both sides

$y+2-2=\frac{1}{6}\left(x-6\right)-2$

$y=\frac{1}{6}x-3$

Therefore, an equation of the line that passes through the point (6, − 2) and is perpendicular to the line will be:

$y=\frac{1}{6}x-3$

5 0

3 years ago

Write the equation of the line in slope-intercept form that passes through the points (-3,3) and (3,-9).

tensa zangetsu [6.8K]

Answer:

m = -2

Step-by-step explanation:

y = -2x - 3

3 0

3 years ago

What is the range of f(x) = A cos(x) +b or<br> g(x) = A sin(x)+b?

vagabundo [1.1K]

Answer:

Step-by-step explanation:

The range of f(x) = cos(x) is [-1, 1].

That of f(x) = A cos(x) is [-A, A], and

That of f(x) = A cos(x) + 2 is [ b-A, b+A ].

The function g(x) = A sin(x)+b has the same range.

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3 years ago