what is the inverse of f(x)=x^3 - 4

Answer 1

The inverse requires that you replace all x’s with y’s and all y’s with x’s; then solve for y.

f(x)=(x^3)-4

y=(x^3)-4 so.....

x=(y^3)-4 then.....

x+4=(y^3)

(x+4)^(1/3)=(y^3)^(1/3)

(x+4)^(1/3)=y or.....

y=(x+4)^(1/3) so.....

[f^(-1)](x)=(x+4)^(1/3)

In words, the inverse of (x^3)-4 is the cubed root of (x+4).

Answer 2

Remember that f(x)= is the same thing as y= so

y = x^3 - 4; we now make it x= so

y - 4 = x^3; take the cubed root to both sides so

(y-4)^^1/3 = x