Question

Let $f\left(x\right)$ be an increasing function defined on $(0,\infty )$. If $f(2a^2+a+1)>f(3a^2-4a+1)$, then the possible integers in the range of $a$ is/are

• A. $1$
• B. $2$
• C. $3$
• D. $4$

Answer 1

Answer: (B), (C), (D)

The correct options are
B $3$
C $2$
D $4$

Given : $f(2a^2+a+1)>f({3a}^2-4a+1)$ and $f\left(x\right)$ is an increasing function defined on $(0,\infty )$.

If it is increasing, then $f\left(x\right)>f\left(y\right)⟹x>y$

So, $(2a^2+a+1)>({3a}^2-4a+1)$

On simplifying, $a<5$ and $a>1$

Therefore, option $B,C$ and $D$ are correct answer.