Inverse function

The inverse of a function is the functions reflection in the line y=x

Look at your graphs.

Let's write

y = 8x^3 - 6       Let's get x by itself   ....  add 6 to both sides

y + 6 = 8x^3      Divide by 8 on both sides

(y + 6) / 8   =   x ^3           Take the cube root of both sides.....

[(y + 6)/ 8]^(1/3)  = x        Now "swap" x and y

[(x + 6)/ 8]^(1/3)  = y        And, for y, write f ^-1(x) and there's the inverse

We can use an informal way to check that this is the inverse - it isn't foolproof, but it will work in most cases.....

Note that the inverse should "reverse" the x and y coordinates on a graph. So, in the original problem, let x = 1 and y will = 2. Then, in the inverse, let x =2, and we should get y =1...and we do!!   So, we're pretty sure it's correct.......