Question

What is the f-1(x) ?

Answer 1

(9x)/(2-2x)

Explanation:

let f-1(x) = y

then, f(y) = x

so, (2y)/(9+2y) = x

***remember the thing inside the () in f(x) can change! y can go in x's place, any number or any other variable can go in x's place! BUT, nothing else can be changed in the function***

now just solve for y!

multiply both sides by (9+2y): 2y = 9x + 2xy

bring the y's together (subtract both sides): 2y-2xy =9x

hey! we can factor the left side (where the y's are): 2y(1-x) = 9x

get all the x's together (divide both sides) : 2y = (9x)/(1-x)

get y alone (divide both sides by 2): (9x)/(1-x) * (1/2)

*finally* distribute/simplify: (9x)/(2-2x)

you can double-check the answer on desmos!

~ lmk if u got Qs :>