Step-by-step explanation:
we have a function, when for every valid x value we get exactly one y value (not 2 or more, not 0, but exactly 1).
x×7 = y⁴
7x = y⁴
y = 4th root(7x)
the 4th root is the square root of the square root.
so, we know, only positive x-values are valid.
but, even when restricting it to positive x-values, a square root as a 4th root (any even grade root) has a positive and a negative solution for the same x-value.
e.g.
x = 7³ = 343
7×343 = 2,401
the 4th root(2,401) = +7 and -7, as +7⁴ = 2,401, and -7⁴ = 2,401.
so, we have 2 different y-values assigned to most x-values (only exception is x=0), and this is therefore not a function.
