If a,b,c,d, and x represent positive real numbers, what is the maximum value of the function f(x)= a[cosb(x+c)]-d?

Answer 1

the cos(anything) has value between -1 and +1
so the max value of cosb(x+c) = 1,
the b controls the frequency, and +c moves it to the left c units. This does not affect the maximum

then the max value of a[cosb(x+d)] is 'a'
but then the function is moved down d units
so the max value of your function is a-d

Answer 2

thank you! that really helped