Find the inverse of f: R→R given by f(x) = x³ – 2
To find the inverse of f(x) = y = x³ – 2
1. switch x and y
x = y³ – 2
2. Solve for y in terms of x
y=∛(x+2)
3. Plot both f(x) and f-1(x) on a graph. They should be mirror images of each other about y=x.
Also, this helps to check the domain and range of f-1(x).
In this case, f-1(x) is still R->R.
OK Thank you!
To find the inverse of the function f(x) = x^3 - 2, we need to follow these steps:
Step 1: Replace f(x) with y: y = x^3 - 2.
Step 2: Swap the x and y variables: x = y^3 - 2.
Step 3: Solve the equation for y: Add 2 to both sides of the equation: x + 2 = y^3.
Step 4: Take the cube root of both sides to isolate y: y = ∛(x + 2).
Therefore, the inverse function of f(x) = x^3 - 2 is f^(-1)(x) = ∛(x + 2).
Note: The inverse function "undoes" the operation of the original function.