Question

1a.) Find the inverse function of f (x) = 1/√x−2. 1b.) Sketch the function and its inverse. You are more than welcome to use Desmos to get some points for your sketch. 1c.) Now graph the line y = x on the same graph above. Using your picture and/or Desmos, what do you notice about the relationship between the function, its inverse, and line line y = x? 1d.) Prove that the function you found in part a, is the inverse function of f (x) = 1/√x−2. 1e.) What is the domain of f (x) = 1/√x−2? What is the domain of its inverse function? 1f.) What is the range of f (x) = 1/√x−2? What is the range of its inverse function?

          1a.) Find the inverse function of f (x) = 1/√x−2.

1b.) Sketch the function and its inverse. You are more than welcome to use Desmos to get
some points for your sketch.

1c.) Now graph the line y = x on the same graph above. Using your picture and/or Desmos,
what do you notice about the relationship between the function, its inverse, and line
line y = x?

1d.) Prove that the function you found in part a, is the inverse function of f (x) = 1/√x−2.

1e.) What is the domain of f (x) = 1/√x−2? What is the domain of its inverse function?

1f.) What is the range of f (x) = 1/√x−2? What is the range of its inverse function?

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Added by Christina A.

Precalculus: Graphs and Models, A Right Triangle Approach

Marvin L. Bittinger, Judith A. Beecher,… 6th Edition

Chapter 5

Instant Answer

Solved by Expert Audrey Fong

01/28/2023

Step 1

f (x) = 1/√x−2 We can use the inverse function rule to find the inverse function: f′(x) = 1/√x−2 We can now use this information to find the inverse function of f (x). Show more…

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1a.) Find the inverse function of f (x) = 1/√x−2. 1b.) Sketch the function and its inverse. You are more than welcome to use Desmos to get some points for your sketch. 1c.) Now graph the line y = x on the same graph above. Using your picture and/or Desmos, what do you notice about the relationship between the function, its inverse, and line line y = x? 1d.) Prove that the function you found in part a, is the inverse function of f (x) = 1/√x−2. 1e.) What is the domain of f (x) = 1/√x−2? What is the domain of its inverse function? 1f.) What is the range of f (x) = 1/√x−2? What is the range of its inverse function?

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Transcript

00:01 In this question, we're given this function, fx.

00:04 And we want to find its inverse function.

00:08 Now, before we do that, let's sketch the function first.

00:19 For fx, we know that x cannot be 2 or less, otherwise it will not be defined.

00:30 So we actually have a vertical as simple here at x equals to 2.

00:37 So the function actually looks like this.

00:40 So this is f.

00:52 So you can see that the domain of f is from 2 to infinity, not inclusive of 2, and the range of f is 0 to infinity.

01:09 Okay, so part 1 or part a want to find the inverse.

01:14 I'm going to let y equals to fx.

01:19 So y is 1 over square root x minus 2.

01:23 I want to express x in terms of y.

01:25 Because for inverse the x and y are interchanged square both sides.

01:41 I'm going to let x become f inverse x and the y will be become x square.

01:50 Now when you express f inverse you must always accompany by its domain.

01:54 Now domain of f inverse is equal to the range of f and there will be 0 to infinity.

02:04 They want us to sketch the f and f inverse.

02:10 So f inverse, so f inverse.

02:11 If you use the semores, you'll know that it will look...

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