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Let f(e) tan-I (€ 2) + 14. Find the domain of the inverse of f(z) and evaluate - the inverse value f-1 (14 + 3)Domain: [14-n/2, 14+1/2], and the inverse value...

Question

Let f(e) tan-I (€ 2) + 14. Find the domain of the inverse of f(z) and evaluate - the inverse value f-1 (14 + 3)Domain: [14-n/2, 14+1/2], and the inverse value= 3 Domain: (-14-n/2, 14+1/2), and the inverse value = 1 Domain: [-14-n/2, 14+n/2],and the inverse value = 1 Domain: (14-1/2, 14+7/2), and the inverse value = 3 Domain: (-0o, oo), and the inverse value = 2 Domain: (14-1/2, 14+7/2), and the inverse value = 2

Let f(e) tan-I (€ 2) + 14. Find the domain of the inverse of f(z) and evaluate - the inverse value f-1 (14 + 3) Domain: [14-n/2, 14+1/2], and the inverse value= 3 Domain: (-14-n/2, 14+1/2), and the inverse value = 1 Domain: [-14-n/2, 14+n/2],and the inverse value = 1 Domain: (14-1/2, 14+7/2), and the inverse value = 3 Domain: (-0o, oo), and the inverse value = 2 Domain: (14-1/2, 14+7/2), and the inverse value = 2



Answers

Find the inverse function $f^{-1}$ of each function $f .$ Find the range of fand the domain and range of $f^{-1} .$ $$f(x)=2 \tan x-3 ;-\frac{\pi}{2}<x<\frac{\pi}{2}$$

The questions is that we have to find the inverse function half in was of the human function F. Which is If X is equal to two 10 x -3 for this question. And also where X ranges from minus by by two, 25 x two. Here, we also need to find this range of the function F. And the domain and arrange of the universe function of this. Now moving towards the solution As it is given, FX is for 2-10 X -3. This is the given function. So effects can be written as why? So 10 X -3. Now after inter changing the places of X. X and Y. That is access opposed to 10 by minus three. We will get are Why is it police to 10 invoice of X plus three by two. That is half inverse of facts. Will report to 10 in worse X plus three by two. So this would be the answer to the first part. Now, moving towards part B where we have to find the domain and range is for the fallen functions. And as we know that the domain of inverse Benjamin function ranges from minus infinity to infinity. So the argument which we got in the above solution should also lie between this strange that is minus infinity X plus three by +22 Infinite solving case. We will get The domain as -10inity to infinite. And as we know that the range of the functional as a response to the domain of the universe function, which we obtained here to be as minus infinity to infinity, and also the range of the universe function, What we call to -5 x 2-5 x two. And so this would be the final solution to the government question. Thank you.

So let's begin by getting the domain and range of this function So the domain is given to us. It's negative one minus pi over two too high over two, minus one. And this is exclusive of the endpoints. And so to get the range here, we know that tangent will give values between negative and Finley animosity all values. And so having a negative side and attracting three won't change. That will still be infinite. Subtracting three doesn't change how high it'll reach. So we know that are arranged here will be negative infinity to infinity since we got attention function. So now let's go ahead and find of inverse. So first, let's take f of X. Let's call it F of X. Why? So we have why equals negative tangent of X plus one minus three. So then, to solve for the inverse function, we switch x and y So we have X because negative tangent of Y plus one minus three. So we need to solve for y. So first will add three. So we have X plus three equals negative tangents. Why close one, then most divide by negative one. So we get negative X minus three equals tangent. Why plus one? Then we'll do inverse tangent on both sides to isolate y plus one. So we get attention in verse of negative X minus three equals why plus one. So then we just attract one, and we will have our function f inverse of axe. So f inverse of X equals inverse tangent of negative X minus three and this is all minus one. So this is our infrastructure in So now to find the domain and range of the inverse function, we use the domain and range from earlier We just swapped them since when we have a function and its inverse the domain arrange are switched. So the domain earlier was negative one minus pi over to two pi over two minus one. So that will become the range of this function. And then similarly, the range of the original function was negative. Infinity to infinity, and that is the domain of our interest function. Wrightson Ella's distract that we have everything done, So we found the range of the original. We found the F inverse function. We found the domain and the range of f inverse using f. So we are done

Impossible function is we need you inter gender X and a Y You mean stand this. Why here would come the X now Echo 23 class dungeon under by this accident becomes the why and the next time we will bring the tree here to do rant on Bubba Say is we want to find out why here and then we should get ex ministry a cultural tension off by why now? The next step is we would think the tension in verse on both side. They're farmers to get attention. Inverse off! Ex ministry Under left on under right. We should get on lead by one. And the last time is we did everything by pi Then why Wicklow Judah Tension in verse off X minus tree. No, they wouldn't buy. And the man for all the attention This one will be the inverse function here. And we know that the man phoned. The tension will be the man for the tension here in verse here. Good bagels from minus infinity to infinity

The question says that we have to find the FN words of the given function F which is FX is equal to minus of 10 X plus one minus three. Where x goes from minus one minus by by two, two, five x 2 -1. And also we have to find the domain and range of the following FN was. And f functions now moving towards the solution. The given function is FX is equal to -10 X-us 1 -3. Now, if X can be written as why is equals 2 -10 X plus one minus three. Now, after inter changing the places of Y index, We can rewrite the question has access close to -10, Y plus one minus three. Now, solving the equation for Y, the value for Y would be equal to y equals two minus 10, inverse x plus three minus one. And this would be the mm fn voice of the effects function and also the solution to the part A of the question. Now moving towards the part B where we have to find the domain of the FN was function and as we know that the domain of inverse tangent function is from minus infinity to infinity. And so the argument we obtained should also lie between this domain that is from minus infinity to infinity, which would be minus infinity to infinity. And so the range oh FF is equals two. Domain of FN was would be from minus infinity to infinity and the range of FN was would be minus one minus by by two, 25 x 2 -1. And this would be the solution to the given question. Thank you.


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