Answer: (b)
Step-by-step explanation:
Given
[tex]f(x)=x^2[/tex]
Now, [tex]f(x)[/tex] is transformed to [tex]g(x)[/tex]
and [tex]g(x)[/tex] is obtained by replacing [tex]x[/tex] with [tex]\frac{x}{2}[/tex] in [tex]f(x)[/tex]
[tex]\therefore g(x)=\left(\dfrac{x}{2}\right)^2\\\\g(x)=\dfrac{x^2}{4}[/tex]
Plot [tex]f(x)[/tex] and [tex]g(x)[/tex] and it can be observed that domain, range, and vertex is same for both the function.
[tex]f(x)[/tex] is narrower compared to [tex]g(x)[/tex]. Therefore, option (b) puts up the invalid reasoning. Hence option (b) is not a true statement.
