inverse of y=(x+6)^3+3
step 1, switch the x and y variables
so ... x = (y+6)^3 + 3
step 2, solve this for y
x-3 = (y+6)^3
(x-3)^(1/3) = y+6
(x-3)^(1/3) - 6 = y
thank you
To find the inverse of a function, we need to swap the roles of x and y and solve for y.
Let's start by swapping x and y in the given equation:
x = (y+6)^3 + 3
Next, we need to solve this equation for y. Here's how we can do that:
Step 1: Subtract 3 from both sides:
x - 3 = (y+6)^3
Step 2: Take the cube root of both sides:
∛(x - 3) = y + 6
Step 3: Subtract 6 from both sides to isolate y:
y = ∛(x - 3) - 6
So, the inverse of the function y = (x+6)^3 + 3 is given by y = ∛(x - 3) - 6.