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Arturiano [62]
3 years ago
9

Please Help!. Consider the function. f (x) = 1/2x +1. a. Find the inverse of f(x) and name it g(x). Show and explain your work.

. b. Use function composition to show that f(x) and g(x) are inverses of each other. . c. Draw the graphs of f(x) and g(x) on the same coordinate plane. Explain how your graph shows that the functions are inverses of each other.
Mathematics
1 answer:
Artist 52 [7]3 years ago
4 0
The inverse of a function is determined by substituting f(x) by y and expressing the function in terms of x = ... Then exchange the places of x and y. In this problem, y = 0.5 x -1; x = 2(y+1) . Then g(x) = y = 2x +2. The graphs are linear but g(x) has a larger slope compared to f(x).
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Quadrant IV: Bottom-right square.

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Answer:

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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3 years ago
IF YOU ANSWER THIS RIGHT NOW ILL GIVE YOU 64 POINTS
Anit [1.1K]

Answer:

13 = x

Step-by-step explanation:

\frac{6}{8} = \frac{(x + 2)}{(x + 7)}

6x + 42 = 8x + 16

42 = 2x + 16

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5 0
2 years ago
What is the distance between point G (4,2) and the line through the points E(1,-2) and F(7, -2)? help please
sineoko [7]

Answer:

4 units

Step-by-step explanation:

Given

G = (4,2)

E = (1,-2); F = (7,-2)

Required

Determine the distance

We need to calculate the equation of EF

But first, we calculate the slope (m)

m = \frac{y_2 - y_1}{x_2 - x_1}

Where

(x_1,y_1) = (1,-2)

(x_2,y_2) = (7,-2)

So:

m = \frac{-2 - (-2)}{7 - 1}

m = \frac{0}{6}

m = 0

The equation is then calculated as:

y - y_1 = m(x - x_1)

Where

m = 0 and (x_1,y_1) = (1,-2)

y - (-2) = 0(x - 1)

y +2 = 0

So, we are to calculate the distance between point G = (4,2) and line y +2 = 0

The distance is calculated using:

d = \frac{|Ax_1 + By_1 + c|}{\sqrt{A^2 + B^2}}

In G = (4,2), we have:

(x_1,y_1) = (4,2)

A general equation has Ax + By + c = 0 as its format

By comparison

A = 0

B = 1

c = 2

d = \frac{|Ax_1 + By_1 + c|}{\sqrt{A^2 + B^2}} becomes

d = \frac{|0 * 4 + 1 * 2 + 2|}{\sqrt{0^2 + 1^2}}

d = \frac{|0 + 2 + 2|}{\sqrt{0 + 1}}

d = \frac{|4|}{\sqrt{1}}

d = \frac{4}{1}

d = 4

<em>Hence, the distance is 4 units</em>

5 0
3 years ago
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