Question

given f(x)=-9+3sqrt(8x+8 on the domain x is greater then -1 find f^-1(x)

Answer 1

the inverse maps each point (x,y) to (y,x) so switch x and y:

x = -9 + 3*sqrt(8y + 8)

so (x + 9)/3 = sqrt(8y + 8)

so (x + 9)^2/9 = 8y + 8

so 8y = (x + 9)^2/9 - 8

so y = (x + 9)^2/72 - 64

so f^-1(x) = (x+9)^2/72 - 64, with domain [-9,infinity) and range (-1, infinity)

Answer 2

oops.

backtrack: 8y = (x + 9)^2/9 - 8

so y = (x + 9)^2/72 - 1

Answer 3

so f^-1(x) = (x + 9)^2/72 - 1, with domain [-9, infinity) and range (-1, infinity)

Answer 4

thanks really appriciate it