Question

( f: R rightarrow R )
( f(x)=x+sin x+7 )
( f^{prime}(x)=1+cos x+0 )
( =1+log x )
We know, ( -1 leq cos x leq 1 Rightarrow-1+1 leq 1+cos x leq 1+1 )
( Rightarrow 0 leq 1+log x leq 2 )
( f^{prime}(x)=1+cos x geqslant 0 )
( #(x) ) is an increasuig function ( therefore ) If is one-one

# (1) Iff: R R be defined as f(x) = x + sinx + 7, then check whether f(x) is one-one or many one

Solution