Given that f(R)=R , g(R)=R be defined respectively by
f(x)= sin x+2 , x>1
= cos x-2 , x<=1
g(x)=2x+3 , x>0
=x^2 , x<=0
Find f o g
we have
2 functions for g(x).
and for
so for
similarly
, and
And
for
Finally
f(g(x))= if
if
if
notice we have covered the whole real line with x. The important part is to use restrictions of x so that g(x) fits in the inequalities for f(x). if i had used
instead of then the next would be which doesn't fit the inequalities for f(x).
[I rushed this there may be mistakes ]