Find the inverse of the function: f(x)= -2(x+2)^3

Answer 1

just switch x and y and solve for the new y

you're given y=-2(x+2)^3, switch and you get

x =-2(y+2)^3, now solve for y

(y+2)^3 =-x/2

y = -2 + (-x/2)^(1/3) = the inverse

f^-1(x) = -2 + cube root of -x/2

you may want to check this with a graphing calculator. graph both equations and visually see if they appear to be reflections across the line y=x

if (x,y) is on the graph of f(x), then (y,x) will be on the graph of the inverse function

y=-2(x+2)^3

for the point (-2, 0) on that graph, (0,-2) will be on the graph of the inverse

-2 = -2+ (-0/2)^(1/3)