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Marysya12 [62]
3 years ago
9

Given the function f(x) = 0.5|x – 4| – 3, for what values of x is f(x) = 7?

Mathematics
1 answer:
Semenov [28]3 years ago
5 0

Answer:

x = - 16, x = 24

Step-by-step explanation:

Given f(x) = 7 then equate f(x) to 7

0.5 | x - 4 | - 3 = 7 ( add 3 to both sides )

0.5 | x - 4 | = 10 ( divide both sides by 0.5 )

| x - 4 | = 20

The expression inside the absolute value bars can be positive or negative, so

x - 4 = 20 ( add 4 to both sides )

x = 24

OR

- (x - 4) = 20

- x + 4 = 20 ( subtract 4 from both sides )

- x = 16 ( multiply both sides by - 1 )

x = - 16

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a) Since the corresponding y-value is -0.6, hence the point (-0.8, -0.6) is a solution to the system of  equations

b) since  the corresponding x-value is not 1/3, hence the point (1/3, 2) is not a solution to the system of  equation

In order to show if the given point corresponds to the given function, we will have to substitute the value of x into the function to see if we will have its corresponding y-value

For the point (-0.8, -0.6), substitute x = -0.8 into both functions as shown:

f(x)  = 2x + 1

f(-0.8) = 2(-0.8) + 1

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f(-0.8) = -0.6

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y = -3(-0.8)- 3

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Since the corresponding y-value is -0.6, hence the point (-0.8, -0.6) is a solution to the system of  equations

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Since the corresponding x-value is not 1/3, hence the point (1/3, 2) is not a solution to the system of  equations

Learn more on systems of equation here: brainly.com/question/847634

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