SOLUTION: Find the inverse function: {{{ y=x^3 +3 }}}

Algebra ->  Functions -> SOLUTION: Find the inverse function: {{{ y=x^3 +3 }}}      Log On


   

Question 996400: Find the inverse function:
+y=x%5E3+%2B3+
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
y = x^3 + 3

set y = x and x = y to get:

x = y^3 + 3

now you need to solve for y.

subtract 3 from both sides of the equation to get:

x - 3 = y^3

take the cube root of both sides of the equation to get:

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

here's a graph of your original equation and the inverse equation.

they are reflections about the line y = x.

if g(x) is the inverse of f(x), then f(x,y) would be equal to g(y,x) as shown in on the graph.

the reflected points will be on the line that is perpendicular to the line y = x.

that would be on the line y = -x + whatever value of x you want as the y-intercept.

in this graph i used a y-intercept of 5 to give me the points shown on the graph.

here's the graph.

$$$