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Nick R.

Calculus 1 / AB

1 week, 5 days ago

what is the inverse of f(x)=7x/(2x-3)


what is the inverse of f(x)=7x/(2x-3)


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Video Transcript

discussion we have given the following function F of X is equal to seven X by two weeks minus three. And we're asked to find the inverse of function inverse of F of X. Uh Let us take uh why perfects what we call to ffx that kind of stuff that given functions, Why? That they called for Fax and that he called seven ex wife who works ministry. No, not one thing to find the inverse. We have one basic rule to find inverse of any function. I am writing it here in Warsaw any function F of X. Can we find, can we uh find by, can we calculated bye by using this principle, wow. The principle is uh replace X with the Y and Y with X. This is the first one and 2nd 1 is solve for Y, solve for Y. So these are the two steps uh you should follow to find the universe of any function F of X. Now north you may not calculate it was for some functions uh If universe exists, then it can be calculated by using these two steps. If it was exists. If inverse is not, does not exist, then we cannot calculate. Now let us try to find the solution of the question by using this principle. See uh this is the actual function We have what we call to have four effects that they call the seven X. Work. So this is the actual function, actual function Yes. Why you called to seven expert who works my industry Now I Step one. The first stop is replace X with Y and Y. We tax. So we have to write X in place of way and Y in place effects. If we write that we can we get X equal to uh seven. Bye bye to buy ministry have replaced Vivatex. And actually, so first step is over now. In second step we should solve for way. No, I am going for step two. Mhm. Uh huh. Yes. See here step two. Uh So now I am taking to a ministry to left side. So it will become X into two x -3 is equal to seven by if you want to play with tax then we get To YX -3 x equal to seven Y. Now if you bring seven right or left side and -3 extra writer we get to YX -7 by He called the three X. If we take white common from these two we get y into two X -7. He called 2 3 X. Uh Now it is uh take two weeks minus 72 right side. We get what equal to three X by ah two X -7. So now we have solved for Y. Finally we have written by in terms of X. So this is the inverse. Aww our politics. So this is the north of Fairfax. We can denote this as f universe sex. And that they call to why. And that will lose three expert to works -7. Therefore the final answer is the universe of a function of fine words. X equal to three. Explain to explain a seven. Uh now you can see both and I am showing both a half accent Fn words affects. What do you see? This is a box, This is a fox and this is F. N. Word suffix. Uh Please note an important thing. FN. Where sex is not equal to one by a carfax, This is not the case, this is strong. FN was actually not equal to one way of affects. We should follow these two steps. These two steps to find the action was step one and step two to find the favors of any function. Thank you.