Question

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

• A. Range of $f\left(x\right)$ is $R^{+}$
• B. $f\left(x\right)$ is many one function
• C. Range of $f\left(x\right)$ is $R$
• D. $f\left(x\right)$ is one one function

Answer 1

Answer: (C), (D)

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

Here, $f\left(x\right)=5x^3+2x+3$, then
$f^{\prime }\left(x\right)=15x^2+2$
for $f^{\prime }\left(x\right)$ discriminant will be negative and $a$ is positive, therefore $f^{\prime }\left(x\right)$ is always positive, hence $f\left(x\right)$ is always increasing function.
Since, $f\left(x\right)$ is a polynomial function with highest power as odd. Therefore, Range of $f\left(x\right)$ will be $R$.