Relations & Functions Questions (810)

JM Q20.

Let \(f:\mathbb{N}\setminus\{1\}\to\mathbb{N}\), \(f(n)=\)highest prime factor of \(n\). Determine nature of \(f\).

\(f(x+y)=f(x)f(y)\), \(f(1)=3\). If \(\sum_{i=1}^n f(i)=363\), find \(n\).

JM Q22.

JM Q33.

Let the range of the function $f(x)=\dfrac{1}{2+\sin3x+\cos3x}$, $x\in\mathbb{R}$ be $[a,b]$. If $\alpha$ and $\beta$ are respectively the A.M. and G.M. of $a$ and $b$, then $\dfrac{\alpha}{\beta}$ is equal to:

●Ex. 16 If f : ℝ → A, where A = {x : −5

The corner points of the feasible region determined by the system of linear constraints are (0, 10), (5, 5), (15, 15), (0, 20). Let z = px + qy. Condition on p and q so that the maximum of z occurs at both the points (15, 15) and (0, 20) is

Let \(f:(1,3)\to\mathbb{R}\), \(f(x)=\dfrac{x[x]}{1+x^2}\). Find the range of \(f\).

JM Q26.