Answer: Option C.
Step-by-step explanation:
For a parent function [tex]f(x)=x^2[/tex], you have these transformations:
If [tex]f(x)=c(x^2)[/tex] and [tex]0 <c <1[/tex] then the graph is compressed vertically by a factor "c".
If [tex]f(x)=c(x^2)[/tex] and [tex]|c| > 1[/tex] then the graph is stretched vertically by a factor "c"
If [tex]f(x)=(cx)^2[/tex] and [tex]0 <c <1[/tex] then the graph is stretched horizontally by a factor "c"
If [tex]f(x)=(cx)^2[/tex] and [tex]|c| > 1[/tex] then the graph is compressed horizontally by a factor "c"
In this problem we have the function [tex]f(x)=x^2[/tex] and we know that this is horizontally compressed to g(x), then the transformation is:
[tex]f(x)=(cx)^2[/tex] and the factor must be [tex]|c| > 1[/tex]
You can observe that the option that shows this form is the option C. Therefore, the equation of g(x) is:
[tex]g(x) = (5x)^2[/tex]
Where [tex]|5| > 1[/tex]
