How To Add Fractions Functions

- we're given f of x = the quantity 5x + 2 divided by the quantity x - 3 and we're asked to find f inverse of x or the inverse of the given function. to remember how to do this,

How To Add Fractions Functions, i think it's important to recognize that the inverse function is going to undo the operation of the original function. for example, if x is the input into the function f

and y is the output, this y becomes the input into the inverse function, which returns the original value of x. which means when we're given the equation of the function we want to find the inverse. the first step is to write the original function in terms of x and y and then we'll interchange the x and y variables. so the original function can be written as

y = (the quantity 5x + 2) divided by (the quantity x - 3). so the inverse function will be x = (the quantity 5y + 2) divided by (y - 3). so this y which is the output of function f is now the input or the x value for the inverse function and these xs which are the inputs of f are now the y values or outputs of the inverse function. and now we're left to solve this for y and then replace y with inverse function notation.

so because the right side is in fraction form we could be this x/1 and then cross multiply meaning ( x x the quantity y) - 3 must equal 1 x the quantity 5y + 2. or we could just multiply both sides by the quantity y - 3. either way we would have x x (the quantity y - 3) = (5y + 2). let's go ahead and clear these parentheses so we'll distribute here.

we have xy - 3x = 5y + 2. now remember our goal here is to solve this for y which means if the term has a y in it we want it on one side and if it doesn't we want it on the other side. let's start by subtracting 5y on both sides. so this would give us (xy - 5y) - 3x = 2. now we'll add 3x to both sides. this is zero,

so now we have xy - 5y is going to be equal to 3x + 2. now to solve this for y we're actually going to have to factor out the common factor of y. so we'll have y x the quantity x - 5 = 3x + 2. now we're one step away, we need to divide both sides by the quantity x - 5. so we have y = quantity 3x + 2 divided by the quantity x - 5. so for our last step,

let's go ahead and replace y with inverse function notation. f inverse of x is equal to quantity 3x + 2 divided by the quantity x - 5. so here's the inverse function that we're asked to find. i hope you found this helpful. â