y = (8 + 9th sqrt of x)^3
I trying to figure out the formula for the inverse of the function. I didn't know how else to express the square root of x with the little 9 in front.
write it this way:
y = (8 + x^(1/9) )^3
2 steps to finding the inverse:
#1. interchange the x and y variables
y = (8 + x^(1/9) )^3 <--- inverses of each other ----> x = (8 + y^(1/9) )^3
#2. Now solve this new equation for y
x^(1/3) = 8 + y^(1/9)
x^(1/3) - 8 = y^(1/9)
y = ( x^(1/3) - 8)^9
checking with x = 512
original:
y = (8 + 512^(1/9) )3
= (8+2)^3 = 1000
use 1000 in the inverse equation:
y = (1000^(1/3) - 8)^9
= (10-8)^9
= 2^9 = 512
This does not "prove" that my answer is correct, it shows with a high probability that I could
be right.
to prove it, note that if g(x) = f-1(x) then
f(g(x)) = g(f(x)) = x
So, I'll do f(g)
f(g) = (8 + g^(1/9) )^3
= (8 + ( x^(1/3) - 8)^9^(1/9) )^3
= (8 + x^(1/3) - 8)^3
= (x^(1/3))^3
= x
Do g(f) similarly