Q:

Find the inverse of the function. y=2x2-4

Find the inverse of the function. y=2x2-4

Accepted Solution

A:
Answer:Step-by-step explanation:The correct way in which to write this function is y = 2x^2 - 4, where ^ indicates exponentiation.1.  Interchange x and y.  From y = 2x^2 - 4 we get x = 2y^2 - 42.  Solve this result for y:  2y^2 - 4 - x =>  2y^2 = x + 4.  Divide both sides by 2       to isolate y^2:      y^2 = (1/2)(x + 4)                                                                               √(x + 4)        Take the square root of both sides:  y = ± --------------                                                                                        √2Note that √(x + 4) is real only for x ≤ 4.  Also (very importantly) note that this formula for y has two distinct values, meaning that it does not represent a function.  If we take only +√(x + 4) and ignore -√(x + 4), then we'll have the function             √(x + 4)                                                                  y = ± ------------------ with the domain restriction x ≥ -4                      √2