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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.

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## 1 Answer

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Toolbox:
• 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

$'False'$

answered Mar 6, 2013 by

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