Question

Let the function be $f:R\to R$ such that$f\left(x\right)=3x^2+8x+5$, then the correct OPTIONS is/are

• A. $f\left(x\right)$ is one one function
• B. Range of $f\left(x\right)$ is $[-\frac{1}{3},\infty )$
• C. $f\left(x\right)$ is many one function
• D. Range of $f\left(x\right)$ is $R$

Answer 1

Answer: (B), (C)

$f\left(x\right)$ is many one function

Here, $f\left(x\right)=3x^2+8x+5$, then
$f^{\prime }\left(x\right)=6x+8$
Since the function is defined from $R$ to $R$
$f^{\prime }\left(x\right)=6x+8$ will be both positive and negative for the given domain, therefore
$f\left(x\right)$ is many one function
For $f\left(x\right)=3x^2+8x+5$
$-\frac{D}{4a}=\frac{-1}{3}$
So, Range of $f\left(x\right)$ will be $[-\frac{1}{3},\infty )$