what is the inverse of the function f(x)=2x2+2?
To find the inverse of a function, you need to follow a few steps:
Step 1: Start with the function f(x) and replace f(x) with y.
y = 2x^2 + 2
Step 2: Swap x and y to exchange their positions.
x = 2y^2 + 2
Step 3: Solve the resulting equation for y.
x - 2 = 2y^2
Step 4: Divide both sides by 2 to isolate y.
(x - 2) / 2 = y^2
Step 5: Take the square root of both sides, considering both the positive and negative square root.
y = ±√[(x - 2) / 2]
So, the inverse of the function f(x) = 2x^2 + 2 is given by:
f^(-1)(x) = ±√[(x - 2) / 2]
Note that the ± symbol represents both the positive and negative square roots, which includes two possible solutions.