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Worksheet 14 Q3 Find the inverse of f(x)=log_(2)(x-1) and the domain of the inverse function. Recall that finding inverse of log function entails rewriting a log expression as an exponeintial expression. Do that to find the inverse of the above function. Write down the steps below: ◻ Now you need to find the domain of the inverse function (which is also the range of the original function). How would you find that out and what would it be? Write the solution below: Worksheet 14 Q3 Find the inverse of f() = log2(x -- 1) and the domain of the inverse function. Recall that finding inverse of log function entails re- writing a log expression as an exponential expression. Do that to find the inverse of the above function. Write down the steps below: VF Now you need to find the domain of the inverse function (which is also the range of the original function). How would you find that out and what would it be? Write the solution below:

          Worksheet 14 Q3
Find the inverse of f(x)=log_(2)(x-1) and the domain of the inverse function.
Recall that finding inverse of log function entails rewriting a log expression as an exponeintial expression. Do that to find the inverse of the above function. Write down the steps below:
◻
Now you need to find the domain of the inverse function (which is also the range of the original function). How would you find that out and what would it be? Write the solution below:
Worksheet 14 Q3
Find the inverse of f() = log2(x -- 1) and the domain of the inverse function.
Recall that finding inverse of log function entails re- writing a log expression as an exponential expression. Do that to find the inverse of the above function. Write down the steps below:
VF
Now you need to find the domain of the inverse function (which is also the range of the original function). How would you find that out and what would it be? Write the solution below:

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worksheet 14 q3 find the inverse of fxlog2x 1 and the domain of the inverse function recall that finding inverse of log function entails rewriting a log expression as an exponeintial expres 39965

Added by Robert M.

Precalculus with Limits

Ron Larson 2nd Edition

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Solved by Expert Keondre Parker

01/27/2023

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The inverse function will be in the form of f^(-1)(x) = 2^x + 1. Show more…

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Worksheet 14 Q3 Find the inverse of f(x)=log_(2)(x-1) and the domain of the inverse function. Recall that finding inverse of log function entails rewriting a log expression as an exponeintial expression. Do that to find the inverse of the above function. Write down the steps below: ◻ Now you need to find the domain of the inverse function (which is also the range of the original function). How would you find that out and what would it be? Write the solution below: Worksheet 14 Q3 Find the inverse of f() = log2(x -- 1) and the domain of the inverse function. Recall that finding inverse of log function entails re- writing a log expression as an exponential expression. Do that to find the inverse of the above function. Write down the steps below: VF Now you need to find the domain of the inverse function (which is also the range of the original function). How would you find that out and what would it be? Write the solution below:

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00:01 All right, so for a, we want to start off by finding the inverse function.

00:06 How we do that is by swapping the x and the y, and then solving for y again.

00:15 So if we're going to multiply both sides by the denominator, divide by x, square both sides, and then add two.

00:40 All right, then for part b, we want to graph the two functions on the same line or on the same graph.

00:46 So if we grab this function, the original, which is the y equals 1 over square root of x minus 2.

00:58 And then if we graph the inverse, which i'm going to do here in blue.

01:17 All right.

01:17 So we see if we have the two graph together.

01:19 So now for part c, they wanted us to graph y equals x on there.

01:28 So we have y equals x line to be here.

01:32 And we see that between the three graphs there's going to be an intersection point right there and that intersection point has to be at 2 .206 comma 2 .206 for d they want us to prove that our inverse is correct how we do that is by composing the two functions is going to be f of f minus one or f inverse of x so in our f function we're going to have one over the square root and now we're going to have our inverse function where our x would be so it's going to be one over x squared plus two and then minus two so we're going to simplify one over the square root of we can rewrite this what the twos are going to cancel.

02:51 So we write this as x to the negative 2.

02:58 Or actually, we can keep that as 1 over x squared.

03:05 So denominator return into just 1 over x or just x.

03:11 So since our composition is equivalent to x, then these two are inversions of each other...

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