Question

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

JEE/Engineering Exams

Maths

Solution

171

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( 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