Question

The graph of the function f(x) = 5 cos (2x) is a reflection over the x-axis of the graph of g(x) =

Answer 1

`g(x)=-5\cos (2x)`

Explanation:

The given function is

`f(x)=5\cos (2x)`

If a function reflected over the x-axis, then x-coordinate remains same but the sign of y-coordinate is changed.

`P(x,y)\Rightarrow P'(x,-y)`

If function f(x) is a reflection over the x-axis to get the of g(x), then the resultant function is

`g(x)=-f(x)`

Substituting the value of function f(x), we get

`g(x)=-5\cos (2x)`

Therefore, the required function is
`g(x)=-5\cos (2x)`.