The functions are:
i) [tex]g(x)=3\cdot \sin(x+ \pi )[/tex]
ii) [tex]f(x)=2 \cos(x)[/tex].
We note that both Sin and Cos functions cannot produces values smaller than -1, or larger than 1.
In other words, the range of both these functions is [-1, 1].
Whatever expression A is, sin(A) and cos(A) are values in [-1, 1].
Assume [tex]\sin(x+ \pi )[/tex] produced its maximal value, 1, then [tex]3\sin(x+ \pi )[/tex] makes this value 3.
Thus, the maximum value of g(x) is 3, as can be also seen in the graph.
Similarly, assume cos(x) produced 1, then 2cos(x) makes it 2. Thus, the greatest value of f(x) is 2.
Answer: max{f(x)}=2, max{g(x)}=3, so g has the largest maximal value.
