If f(x) = sin x and g(x) = cos x, then find (gof)(x) and (fog)(x).

Solution:

A function is a process or a relation that associates each element 'a' of a non-empty set A , at least to a single element 'b' of another non-empty set B. A relation f from a set A (the domain of the function) to another set B

(the co-domain of the function) is called a function in math. 

Given functions are:

f(x) = cosx and g(x) = cos x

Given f:R → R and g:R → R,

Therefore,

fog: R→R and gof: R→R

fog(x) = f(g(x)) = f(cosx) = sin(cosx)

gof(x) = g(f(x)) = g(sinx) = cos(sinx)

If f(x) = sin x and g(x) = cos x, then find (gof)(x) and (fog)(x).

Summary:

If f(x) = sin x and g(x) = cos x, then the values of (gof)(x) and (fog)(x) are sin(cosx) and cos(sinx) respectively.