ANSWER
[tex]g(x) = (4 {x)}^{2} [/tex]
EXPLANATION
We were given that,
[tex]f(x) = {x}^{2} [/tex]
Let
[tex]g(x) = a \times f(x)[/tex]
Or
[tex]g(x) = a {x}^{2} [/tex]
The point (1,16) is on the graph of g(x), hence it must satisfy its equation:
This implies that,
[tex]a {(1)}^{2} = 16[/tex]
[tex]a = 16[/tex]
We substitute the value of 'a' to get,
[tex]g(x) = 16 {x}^{2} [/tex]
Or
[tex]g(x) = (4 {x)}^{2} [/tex]
The correct choice is B.
