List of top Mathematics Questions on Relations and functions asked in AIEEE

Let f be a function defined by $f\left(x\right) = \left(x-1\right)^{2 }+ 1, \left(x \ge 1\right)$. The set $\left\{x : f\left(x\right) = f^{-1}\left(x\right)\right\} =\left\{ 1, 2\right\}$ f is a bijection and $ f^{-1}\left(x\right) = 1+\sqrt{x-1}, x \ge 1.$

A real valued function $f (x) $.Satisfies the functional equation $f(x- y) =f (x) f(y)-f(a-x) f(a+y)$ where a is a given constant and $f(0) = 1$. Then $f(2a - x)$ is equal to

Let $R = \{(1, 3), (4, 2), (2, 4), (2, 3), (3, 1)\}$ be a relation on the set $A = \{1, 2, 3, 4\}$. The relation R is

If $f: R \rightarrow S $ defined by $ f(x)=\sin x-\sqrt{3} \,\cos\,x+\,$ 1, is onto, function then S = ?

The graph of the function $y = f(x) $is symmetrical about the line $x = 2$, then