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QuestionFind thee inverse Lapluce trnnsform ot F()MATH 256...

Question

QuestionFind thee inverse Lapluce trnnsform ot F()MATH 256

Question Find thee inverse Lapluce trnnsform ot F() MATH 256



Answers

Find the inverse of the functions.
$f(x)=4-2 x^{3}$

This question asked us to find the inverse of the function. Four minus X cubed. First stop is flip accident. Why in the equation? Then bring the Y term over to the left hand side. You have y cubed is for minus acts, and that's that. Why is equivalent to the cube droop of four minus X and then lastly interchange. Why substitute this with inverse function of X? Because again we found the inverse is a couple into the cube dripped off for minus tax.

This question asked us to find the emphasis of the function. What we knows the first step is flip accident. Why? Then we know we're gonna be taking the square root of both sides to get to y. Plus one is X squared. And then we know that we want to try to eventually get wide by itself. So we have to wise export minus one. Divide both sides by two when we get wise. Expert minus one over two Lastly interchange. Why? With inverse function of acts.

Yeah. If you draw the graph of this function it is decreasing and hence it is one to work. Next we consider the creating Y echoes flax or eric's miners too. We multiply both sides by X -2. Then we add too white to both sides. And the sub tract four X. From both sides. And this is X times 1 -4 equals to one. So x equals two y. over why miners full enhance the inverse function. Yes. two eggs over its minus four. Next we very fair condition A. And B. Have inverse. Our fax echoes two times my actual were expires too. My actual were ex miners. To my nurse for the just sets multiply both numerator and denominator by ex miners too. And this becomes a detox over eight which we call the. And next F F inverse acts just a substitute Alex cfx with the expression of f universal access. They multiply both the numerator and the denominator by gas miners for Which also enclose 80 x over eight which is X.

So we're trying to find the inverse function off the given equation off of acts equals four to the X power. So let's rewrite this as why equals four to the X and so on Interest function we want to do is you want to swap the places of the X and Y variables to now we get X equals for to the y. C. All I did was simply switched the locations and nothing else. And then next want to isolate the why on one side? And in order to do that, you should move onto law. You should use luck. So do that. You take the base, which is four, and then you take the arguments component just acts. So it's locked base for of X, and we set this equal to power power. Which is why so in this sense, we have created our final answer. The inverse function of F of X is equal to log base for of X. Uh, that's what is the answer


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