Question

$S_1:$ A function is inversible if it is one-one.
$S_2:$ Let $f$ and $g$ be two function $R\to R$ such that $gof$ is one-one then $f$ must be one-one.
$S_3:$ Fundamental period of $\sin x$ is $1$. Where $\{.\}$ represent fractional part functions.
$S_1:$ If $f:R\to R$ is an odd functions then $f(-x)=-f\left(x\right),\forall xϵR$.

• A. $TTFF$
• B. $TTFT$
• C. $FTTF$
• D. $FTTT$

Answer 1

The correct option is D $FTTT$

A function is inversible if it is both one-one ond onto.

Let $f$ and $g$ be two function $R\to R$ Such that $g0f$ is one- one then $f$ must be one-one.

$S_2\to$ True

Fundamental period of $\left\{\sin x\right\}$is 1 .

$S_3\to$ True

If $f:R\to R$ is an odd functions

then $f(-x)=-f\left(x\right)$

$S_4\to$ True

Hence, $FTTT$