00:01
We're given a function rx and we told rx is equal to 8x minus 6 over 7 x plus 8.
00:15
And we are asked to find and simplify the inverse of that function.
00:27
Right? okay, to find and to simplify the inverse of this function.
00:34
So we do a couple steps.
00:38
The first step is a pretty straightforward step.
00:42
Very easy.
00:43
So we're going to rewrite rx as y.
00:51
Very simple.
00:52
Just rewrite the equation.
00:55
And so that would be y equals to 8x minus 6 over 7x plus 8.
01:07
Step 2 would be 2.
01:13
Replace x and y and rewrite the function not the equation sorry this when we're replacing x and y it's going to be instead of y we're going to have x here and every place you see x you're going to put y so x here would be equal to 8 y okay minus six over seven y plus eight that's that's it right so all we did the step two was just to replace the xes and the y so wherever we saw x we put y where we saw y we put x so step three will be the longer one right will be to solve for y so first thing we will do is to well look at the denominator is 7y plus x so let's multiply both sides by 7y plus 8 so we're going to have x times 7y plus 8 on the left inside and we have 8y minus 6 of 7y plus 8 times 7y plus 8 okay and so if you see this would cross off from basic algebra and then we would have x times 7y plus 8 it would be equal to 8 y minus 6 okay now we're going to distribute x here and we'll distribute x what we're going to get is 7x y plus 8 plus 8x will be equal to 8y minus 6.
03:26
So the next thing we're going to do is to, well, we'll move all the terms with y to one side and every other term to a different side, right? and that would just be 7x, y, and, you know, we'll subtract both sides, from both sides, 8y.
03:49
So we're going to have minus 8y.
03:52
You subtract 8 y over here it's going to just be 0 so that just becomes minus 6 up minus 8 x okay so we factorize and we're going to have y okay 7x minus 8 should equal to i mean you can factorize here too um negative 1 um times 6 plus 8x.
04:31
Okay, we could factorize here too.
04:34
Might not be very necessary, so we'd see.
04:39
But we'll now solve for y...