What is the inverse function of....
f(x) = x^3 - 1
Whats the easiest way to solve this?
Can I solve for 'x' first... Then switch 'x' and 'y'. Or do I have to switch 'x' and 'y' from the start?
To find the inverse function of f(x) = x^3 - 1, you can follow these steps:
1. Start by replacing f(x) with y.
y = x^3 - 1
2. Switch the x and y variables.
x = y^3 - 1
3. Solve the equation for y by isolating it.
x + 1 = y^3
4. Take the cube root of both sides to solve for y.
y = (x + 1)^(1/3)
5. Finally, replace y with f^(-1)(x) to express the inverse function.
f^(-1)(x) = (x + 1)^(1/3)
Therefore, the inverse function of f(x) = x^3 - 1 is f^(-1)(x) = (x + 1)^(1/3).
You can solve for 'x' first and then switch 'x' and 'y', or you can switch 'x' and 'y' from the start. Both methods will give you the same answer.
However, it's worth noting that when switching 'x' and 'y' later, you need to make sure to solve for 'y' as the dependent variable instead of 'x'. This is because the inverse function represents the original function reversed, so 'x' becomes the independent variable and 'y' becomes the dependent variable.