MATH SOLVE

2 months ago

Q:
# 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