List of top Mathematics Questions on Composition of Functions and Invertible Function

Assertion (A): The relation R = (x, y) : (x + y) is a prime number and x, y in N is not a reflexive relation. 
Reason (R): The number \( 2n \) is composite for all natural numbers \( n \).
 

What rebate in price of the calculator should the store give to maximise the revenue?
Check whether the relation \( S \) in the set of real numbers \( \mathbb{R} \), defined by:

\[ S = \{(a, b) \mid a - b + \sqrt{2} \text{ is an irrational number} \} \] is reflexive, symmetric, or transitive.
Let \( A = \mathbb{R} - \{5\} \) and \( B = \mathbb{R} - \{1\} \). Consider the function \( f : A \to B \), defined by: \[ f(x) = \frac{x - 3}{x - 5} \] Show that \( f \) is one-one and onto.
The volume of a cube is increasing at the rate of \( 6 \, \text{cm}^3/\text{s} \). How fast is the surface area of the cube increasing, when the length of an edge is \( 8 \, \text{cm} \)?
If \(f(x)=e^x\) and \(g(x)=log_{e}{x}=lnx  \) then \((gof)(x) \) is