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True or False: Let $f:R \rightarrow R$ be the function defined by f(x)=sin (3x+2)$\quad x\in R$.Then f is invertible.

1 Answer

  • 1.A function f is invertible if f is one -one (ie) $ f(x)=f(y)=>x=y \qquad x \in R$ and f is onto
  • (ie) for every $ y\in R $ there exists $ x \in R$ such that f(x)=y
$f:R \to R$
$f(x)=\sin (3x+2) \qquad x \in R$
let $f(x_1)=f(x_2)$
$\sin (3x_1+2)=\sin (3x_2+2)$
$=> 3x_1+2=2x\pi +3x_2+2$
Therefore it does not imply $x_1=x_2$
Therefore f is not one one
f is not invertible



answered Mar 6, 2013 by meena.p

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