if f(x)=x^3-7/2 find f^-1(X)
x = y^3 - 7/2
x + 7/2 = y^3
f^-1(x) = y = ∛(x + 7/2)
To find the inverse of a function, we need to interchange the roles of x and y and solve for y.
Let's start with the given function: f(x) = (x^3 - 7) / 2.
Step 1: Replace f(x) with y: y = (x^3 - 7) / 2.
Step 2: Swap x and y: x = (y^3 - 7) / 2.
Step 3: Solve the equation for y.
To do this, we'll isolate y by multiplying both sides of the equation by 2: 2x = y^3 - 7.
Now, add 7 to both sides of the equation: 2x + 7 = y^3.
And finally, take the cube root of both sides to solve for y: y = ∛(2x + 7).
Therefore, the inverse function is f^(-1)(x) = ∛(2x + 7).