MCQ_SINGLE

Let \(f:R_{+}\rightarrow[-5,\infty)\) be defined as \(f(x)=9x^{2}+6x-5\), where \(R_{+}\) is the set of all non-negative real numbers. Then, f is:

LA

Show that the relation $R$ in the set $A = \{1, 2, 3, 4, 5\}$ given by $R = \{(a, b) \in A : |a - b| \text{ is even}\}$, is an equivalence relation. Show that all the elements of $\{1, 3, 5\}$ are related to each other and all the elements of $\{2, 4\}$ are related to each other, but no element of $\{1, 3, 5\}$ is related to any element of $\{2, 4\}$.

LA

Let $f, g : N - \{1\} \to N$ be functions defined by $f(a) = \alpha$, where $\alpha$ is the maximum of the powers of those primes $p$ such that $p^\alpha$ divides $a$, and $g(a) = a + 1$, for all $a \in N - \{1\}$. Then, check whether the function $f + g$ is one-one or onto. [Competency]

VSA

Let $A = \{x, y, z\}, B = \{u, v, w\}$ and $f : A \to B$ be defined by $f(x) = u, f(y) = v, f(z) = v$. Then check whether $f$ is one-one or onto. [Competency]

VSA

Let $f:A\rightarrow B$ be defined by $f(x)=\frac{x-2}{x-3}$ where $A=R-\{3\}$ and $B=R-\{1\}$. Discuss the bijectivity of the function.

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