SA

Let $D$ be the domain of the real valued function $f$ defined by $f(x) = \sqrt{25 - x^2}$. Then, write $D$.

LA

A function $f : R - \{-1, 1\} \to R$ is defined by: $f(x) = \frac{x}{x^2 - 1}$. (i) Check if $f$ is one-one. (ii) Check if $f$ is onto. Show your work. [Competency]

SA

Let $A = R - \{2\}$ and $B = R - \{1\}$, consider the function $f : A \to B$ defined by $f(x) = \frac{x - 1}{x - 2}$. Is $f$ one-one and onto? [All India 2019]

SA

Prove that the greatest integer function $f : R \to R$ given by $f(x) = [x]$, is neither one-one nor onto, where $[x]$ denotes the greatest integer less than or equal to $x$. [Competency]

VSA

Find the number of one-one onto mapping from $A$ to $B$, where $n(A) = 5, n(B) = 6$.

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