4 By comparing fx withx and fx algebraically determine wheth

4. By comparing f-x) with(x) and -f(x), algebraically determine whether the function f(x)-5+xcosx is even, odd, or neither 5. Find the inverse of the function f(x)-1 algebraically. 2 2. I+ 2

Solution

4)
f(x)=5+xcosx
f(-x) can be found by replacing x with -x
so,
f(-x)=5+(-x)cos(-x)
f(-x)=5-xcos(-x)

cos(-x)=cos(x)
so,
f(-x)=5-xcosx

f(x) is not equal to f(-x) and
f(x) is not equal to -f(-x)
hence it is neither even nor odd