Question

If $f:R\to R$ defined by $f\left(x\right)=2x+5$, if $x>0;f\left(x\right)=3x-2$, if $x\le 0:$ then $f$ is

• A. a function
• B. one one
• C. onto
• D. one- one and onto

Answer 1

Answer: (B)

one one

$f:R\to R$
$f\left(x\right)=2x+5x>0$
$=3x-2x<0$
$f^{\prime }\left(x\right)=2x>0$
$=3x<0$
$f\left(x\right)$ is monotonic increasing,
Every monotonic function is one-one.
$f\left(x\right)$ is not onto because its range is not equal to its co-domain.