Question

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

$f(x)=\frac{3x^2+4x+5}{x^2+5x+9}$
$D<0,a>0\Rightarrow f(x)$ is always positive
$D<0,a>0\Rightarrow R_f\ne R/f$ is into
$\text{ Also, }\frac{3x^2+4x+5}{x^2+5x+9}=\frac{5}{9}$
$22x^2+11x=0$
$11x(2x+1)=0$
$x=0,\frac{-1}{2}$
$\Rightarrow f(0)=f\left(\frac{-1}{2}\right)=\frac{5}{9}\Rightarrow \text{ f is many one }$