Question

# For the following, $y$ can be a function of $x$, $\left( {x \in R,y \in R} \right)?$${y^2} = 4ax$

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Hint:A function is a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output. It is denoted as $f:{\text{X}} \to {\text{Y}}$, a function from X to Y.
It means that if the object x is in the set of inputs (called the domain) then the function f will relate to exactly one object f(x).

Given, $x \in R,y \in R$ and a relation in between x and y as: ${y^2} = 4ax \Rightarrow y = 2\sqrt {ax} .......\left( i \right)$
Thus, by definition of function, each set of values of inputs has a set of possible outputs, i.e., If $x = 0$ , then $y = 2\sqrt {a.0} = 0$
If $x = 1$, then $y = 2\sqrt {a.1} = 2\sqrt a$
If $x = a$, then $y = 2\sqrt {a.a} = 2a$…… etc.
Hence, ${y^2} = 4ax$ is a function of x.