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Please I don’t understand this at all

Please I don’t understand this at all-example-1
User Csnate
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1 Answer

6 votes

Answer: Choice C

f(x) = 13x-7 and g(x) = (x+7)/13

==================================================

Step-by-step explanation:

Let's go through the answer choices to see which pairs are inverses or not.

The process of finding an inverse follows these steps

  1. Replace f(x) with y
  2. Swap x and y
  3. Solve for y to determine the inverse g(x)

-------------------------------

Choice A

f(x) = (x/3) + 10

y = (x/3) + 10 .... f(x) replaced with y

x = (y/3) + 10 .... x and y swapped; solve for y from here

x-10 = y/3

y = 3(x-10)

y = 3x-30

g(x) = 3x-30

This doesn't match the g(x) = 3x-10 listed. We can rule out choice A.

-------------------------------

Choice B

f(x) = cube root of 4x

y = cube root of 4x

x = cube root of 4y

x^3 = 4y

4y = x^3

y = (1/4)x^3

g(x) = (1/4)x^3

This is close to what is listed, but the 4 is not being cubed. We can rule out choice B as well.

-------------------------------

Choice C

f(x) = 13x-7

y = 13x-7

x = 13y-7

x+7 = 13y

13y = x+7

y = (x+7)/13

g(x) = (x+7)/13

This is a perfect match to what choice C is saying. Therefore, choice C is the final answer. If you applied this process in reverse, you'd find that g(x) leads to the inverse f(x).

Further confirmation would be to show that f(g(x)) = x and g(f(x)) = x for all real numbers x. I'll let you do this step.

-------------------------------

For the sake of completion, let's check choice D

f(x) = (9/x) - 5

y = (9/x) - 5

x = (9/y) - 5

x+5 = 9/y

y(x+5) = 9

y = 9/(x+5)

g(x) = 9/(x+5)

Choice D lists (x+5)/9 instead of 9/(x+5), so we can rule out choice D.

User Omegasbk
by
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