MCQ_SINGLE

A function \(f:R_{+}\rightarrow R\) (where \(R_{+}\) is the set of all non-negative real numbers) defined by \(f(x)=4x+3\) is:

SA

A relation R on set $A=\{1,2,3,4,5\}$ is defined as $R=\{(x,y):|x^{2}-y^{2}|

MCQ_SINGLE

Let A = { (α, β) ∈ R x R : |α - 1| ≤ 4 and |β - 5| ≤ 6} and B = { (α, β) ∈ R × R: 16(α-2)²+9(β-6)² ≤ 144}. Then

SA

Let $A=\mathbb{R}-\{3\}$ and $B=\mathbb{R}-\{1\}$. A function $f:A\rightarrow B$ is defined by $f(x)=(\frac{x-2}{x-3})$. Find whether f is one-one and onto.

SA

If $f:R^{+}\rightarrow R$ is defined as $f(x) = \log_{a} x$ ($a > 0$ and $a\ne1$), prove that f is a bijection. ($R^{+}$ is a set of all positive real numbers.)

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