Draw the Graph of Piecewise Function f(x) Draw the Graph of the Function \(f(x)\) Question The function \(f\) is defined by \[ f(x)= \begin{cases} 1-x, & x0 \end{cases} \] Draw the graph of \(f(x)\). Solution The function is defined in three parts. Case 1: \(x0\), the point at \(x=0\) is not included. Therefore, draw an […]

Find (2f + g – h)(1) and (2f + g – h)(0) Find \((2f + g – h)(1)\) and \((2f + g – h)(0)\) Question If \(f, g, h\) are real functions defined by \[ f(x)=\sqrt{x+1} \] \[ g(x)=\frac{1}{x} \] \[ h(x)=2x^2-3 \] then find the values of \[ (2f+g-h)(1) \] and \[ (2f+g-h)(0) \]

Operations on Functions f(x)=log(1-x) and g(x)=[x] Operations on Functions \(f(x)=\log(1-x)\) and \(g(x)=[x]\) Question If \[ f(x)=\log(1-x) \] and \[ g(x)=[x] \] then determine each of the following functions: (i) \(f+g\) (ii) \(fg\) (iii) \(\frac{f}{g}\) (iv) \(\frac{g}{f}\) Also, find \((f+g)(-1)\), \((fg)(0)\), \(\left(\frac{f}{g}\right)\left(\frac12\right)\), \(\left(\frac{g}{f}\right)\left(\frac12\right)\) Solution Given \[ f(x)=\log(1-x) \] and \[ g(x)=[x] \] Here, \([x]\) denotes the

Operations on Functions f(x)=√(x+1) and g(x)=√(9-x²) Operations on Functions Question Let \(f, g\) be two real functions defined by \[ f(x)=\sqrt{x+1} \] \[ g(x)=\sqrt{9-x^2} \] Describe each of the following functions : (i) \(f+g\) (ii) \(g-f\) (iii) \(fg\) (iv) \(\frac{f}{g}\) (v) \(\frac{g}{f}\) (vi) \(2f-\sqrt{5}g\) (vii) \(f^2+7f\) (viii) \(\frac{5}{g}\) Solution Given \[ f(x)=\sqrt{x+1} \] \[ g(x)=\sqrt{9-x^2}

Find g(x) from Piecewise Function g(x)=f(|x|)+|f(x)| Find \(g(x)\) if \(g(x)=f(|x|)+|f(x)|\) Question If \(f(x)\) be defined on \([-2,2]\) and is given by \[ f(x)= \begin{cases} -1, & -2 \le x \le 0 \\ x-1, & 0 < x \le 2 \end{cases} \] and \[ g(x)=f(|x|)+|f(x)| \] Find \(g(x)\). Solution Given \[ f(x)= \begin{cases} -1, & -2

Find f+g, f-g, cf, fg, 1/f and f/g | Functions Class 11 Maths Find f+g, f-g, cf (c ∈ R, c ≠ 0), fg, 1/f and f/g in each of the following. (i) \(f(x)=x^3+1\) and \(g(x)=x+1\) 1. Find \(f+g\) \[ (f+g)(x)=f(x)+g(x) \] \[ =(x^3+1)+(x+1) \] \[ =x^3+x+2 \] 2. Find \(f-g\) \[ (f-g)(x)=f(x)-g(x) \] \[

Find (f + g), (f − g), (fg), and (f/g) with Domain | Class 11 Functions Let f(x) = 2x + 5 and g(x) = x² + x. Describe (i) f+g (ii) f−g (iii) fg (iv) f/g and find the domain in each case. Solution Given: \[ f(x)=2x+5 \] \[ g(x)=x^2+x \] (i) Find \(f+g\)

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, $$