Question

If f:
RR defined by
f(x) = 7 +cos(5x +3) VX ER then
the period of f(x) is​

Answer 1

f(x)=7+cos(5x+3)

Adding a constant term to a function shifts the graph above, but doesn't change the period of the function.

So, the period of the function is same as that of the period of the function cos(5x+3)

Adding the term 3 inside the angle whose cosine is taken, shifts the graph in the left direction, without affecting the period.

So, the period ultimately has to be taken of cos(5x)

Since the period of cos(x) is 2π, the period of cos(nx) would be

n

2π

The answer thus becomes

5

2π