Answer:
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 - 4
2. 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 = ± --------------
√2
Note 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