Question

If $f: R \rightarrow R$ is a function defined as $f(x)=\frac{3 x^2+4 x+5}{x^2+5 x+9}$, then $f$ is

• A. one one, into function
• B. many one, into function
• C. one one, onto function
• D. many one, onto function

Answer 1

Answer: (B)

$f(x)=\frac{3 x^2+4 x+5}{x^2+5 x+9}$
$D <0, a >0 \Rightarrow f ( x )$ is always positive
$D <0, a >0 \Rightarrow R _{ f } \neq R \not f$ is into
$\text { Also, } \frac{3 x^2+4 x+5}{x^2+5 x+9}=\frac{5}{9} $
$ 22 x^2+11 x=0$
$11 x(2 x+1)=0 $
$ x=0, \frac{-1}{2} $
$\Rightarrow f(0)=f\left(\frac{-1}{2}\right)=\frac{5}{9} \Rightarrow \text { f is many one }$