Find the inverse of the function
f(X)= 2x^2 - 3
y = 2x^2 - 3
inverse:
x = 2y^2 - 3
2y^2 = x+3
y^2 = (x+3)/2
y = ± √( (x+3)/2 )
btw, the inverse is not a function
since f is not single-valued, it has no inverse.
For x>=0,
f^-1(x) = √((x+3)/2)
There is also a branch for x <= 0
sorry. The branches split at x = -3, not x=0.
To find the inverse of a function, you need to interchange the x and y variables and solve for y. Let's call the inverse function f^(-1)(x).
Step 1: Replace f(x) with y.
y = 2x^2 - 3
Step 2: Swap the x and y variables.
x = 2y^2 - 3
Step 3: Solve for y.
x + 3 = 2y^2
(x + 3)/2 = y^2
√((x + 3)/2) = y or -√((x + 3)/2) = y
Therefore, the inverse of the function f(x) = 2x^2 - 3 is f^(-1)(x) = √((x + 3)/2) or f^(-1)(x) = -√((x + 3)/2).