Total Number of Functions from A to B Total Number of Functions from A to B Question: Let \(A\) and \(B\) be any two sets such that $$ n(A)=p \quad \text{and} \quad n(B)=q $$ Then the total number of functions from \(A\) to \(B\) is equal to ? Solution A function from \(A\) to \(B\) […]

Find the Domain and Range of f(x)=√(x²-16) Find the Domain and Range of \(f(x)=\sqrt{x^2-16}\) Question: Find the domain and range of the real valued function: $$ f(x)=\sqrt{x^2-16} $$ Solution Domain For a square root function, the expression inside the root must be non-negative. Therefore, $$ x^2-16\ge0 $$ $$ (x-4)(x+4)\ge0 $$ This is true when $$

Find the Domain and Range of f(x)=1/√(16-x²) Find the Domain and Range of \(f(x)=\frac1{\sqrt{16-x^2}}\) Question: Find the domain and range of the real valued function: $$ f(x)=\frac1{\sqrt{16-x^2}} $$ Solution Domain Since the square root is in the denominator: (i) The expression inside the root must be positive. (ii) The denominator cannot be zero. Therefore, $$

Find the Domain and Range of f(x)=-|x| Find the Domain and Range of \(f(x)=-|x|\) Question: Find the domain and range of the real valued function: $$ f(x)=-|x| $$ Solution Domain The modulus function is defined for every real number. Hence, the domain is: $$ \mathbb{R} $$ Range Since $$ |x|\ge0 $$ Therefore, $$ -|x|\le0 $$

Find the Domain and Range of f(x)=|x-1| Find the Domain and Range of \(f(x)=|x-1|\) Question: Find the domain and range of the real valued function: $$ f(x)=|x-1| $$ Solution Domain The modulus function is defined for every real number. Hence, the domain is: $$ \mathbb{R} $$ Range Since modulus values are always non-negative, $$ |x-1|\ge0

Find the Domain and Range of f(x)=(x-2)/(2-x) Find the Domain and Range of \(f(x)=\frac{x-2}{2-x}\) Question: Find the domain and range of the real valued function: $$ f(x)=\frac{x-2}{2-x} $$ Solution Domain Given: $$ f(x)=\frac{x-2}{2-x} $$ The denominator cannot be zero. Therefore, $$ 2-x\ne0 $$ $$ x\ne2 $$ Hence, the domain is: $$ \mathbb{R}-\{2\} $$ Range Simplify

Find the Domain and Range of f(x)=√(x-3) Find the Domain and Range of \(f(x)=\sqrt{x-3}\) Question: Find the domain and range of the real valued function: $$ f(x)=\sqrt{x-3} $$ Solution Domain For a square root function, the expression inside the root must be non-negative. Therefore, $$ x-3\ge0 $$ $$ x\ge3 $$ Hence, the domain is: $$

Find the Domain and Range of f(x)=√(x-1) Find the Domain and Range of \(f(x)=\sqrt{x-1}\) Question: Find the domain and range of the real valued function: $$ f(x)=\sqrt{x-1} $$ Solution Domain For a square root function, the expression inside the root must be non-negative. Therefore, $$ x-1\ge0 $$ $$ x\ge1 $$ Hence, the domain is: $$

Find the Domain and Range of f(x)=(ax-b)/(cx-d) Find the Domain and Range of \(f(x)=\frac{ax-b}{cx-d}\) Question: Find the domain and range of the real valued function: $$ f(x)=\frac{ax-b}{cx-d} $$ Solution Domain Given: $$ f(x)=\frac{ax-b}{cx-d} $$ The denominator cannot be zero. Therefore, $$ cx-d\ne0 $$ $$ x\ne\frac{d}{c} $$ Hence, the domain is: $$ \mathbb{R}-\left\{\frac{d}{c}\right\} $$ Range Let

Find the Domain and Range of f(x)=(ax+b)/(bx-a) Find the Domain and Range of \(f(x)=\frac{ax+b}{bx-a}\) Question: Find the domain and range of the real valued function: $$ f(x)=\frac{ax+b}{bx-a} $$ Solution Domain Given: $$ f(x)=\frac{ax+b}{bx-a} $$ The denominator cannot be zero. Therefore, $$ bx-a\ne0 $$ $$ x\ne\frac{a}{b} $$ Hence, the domain is: $$ \mathbb{R}-\left\{\frac{a}{b}\right\} $$ Range Let