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spayn [35]
3 years ago
9

Identify the inverse g(x) of the given relation f(x). f(x) = {(8, 3), (4, 1), (0, –1), (–4, –3)}

Mathematics
1 answer:
Keith_Richards [23]3 years ago
3 0

Answer:

The inverse g(x) = 2x + 2

Step-by-step explanation:

* Lets explain the inverse of a function

- To find the inverse of any function we switch the x and y then

 we solve to find the new y

- The domain of the function is the values of x and the range of

 the function is the values of y

- The domain of the inverse function is the values of y and the

 range of the inverse function is the values of x

- Lets solve the problem

∵ f(x) = {(8 , 3) , (4 , 1) , (0 , -1) , (-4 , -3)}

- To find the inverse g(x) lets find f(x) from the order pairs

∵ x-coordinates are decreases by 4 and y-coordinates are

  decreases by 2

∴ The relation represents the linear function

- The form of the linear function is f(x) = mx + c , where m is the

  slope of the line and c is the y-intercept

∵ The slope of the line whose endpoints are (x1 , y1) and (x2 , y2)

  is m = (y2 - y1)/(x2 - x1)

- We can find the slope from any two order pairs

∵ (x1 , y1) = (8 , 3) and (x2 , y2) = (4 , 1)

∴ m = [1 - 3]/[4 - 8] = -2/-4 = 1/2

∵ f(x) = mx + c

∴ f(x) = 1/2 x + c

- The y-intercept means the line intersect the y-axis

  at point (0 , c)

∵ There is a point (0 , -1)

∴ c = -1

∴ f(x) = 1/2 x - 1

- To find the inverse of the function switch x and y and solve to

  find the new y

∵ y = 1/2 x - 1 ⇒ switch x and y

∴ x = 1/2 y - 1 ⇒ add 1 to both sides

∴ x + 1 = 1/2 y ⇒ Multiply both sides by 2

∴ 2(x + 1) = y

∴ y = 2x + 2

∵ g(x) is the inverse of f(x)

∵ The inverse of f(x) is 2x + 2

∴ g(x) = 2x + 2

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Answer:

1. 16π

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Step-by-step explanation:

Area of a circle = πr^2

Substitute...

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Answer:

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<em>Presence of walnut leaves in the soil is the </em><u><em>independent variable</em></u>

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<u><em></em></u>

Step-by-step explanation:

<em>An independent variable is the variable in an experiment that can be altered to test for a certain result. It is independent, or does not change with change in other factors in the experiment.</em> In this case, the presence or absence, or quantity of walnut available in the soil is the independent variable in the experiment.

<em>A dependent variable varies, and depends on the independent variable. It is what is measured in the experiment.</em> In this case, the height of the tomato plants is the dependent variable that depends on the presence, absence or quantity of walnut in the soil.

<em>A control in an experiment, is a replicate experiment, that is manipulated in order to be able to test a single variable at a time.</em> Controls are variables are held constant so as to minimize their effect on the system under study. In this case, some of the tomato plants are planted without walnut in the soil, to test the effect of the absence of the walnut in the soil.

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Answer:

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