Let f(x) = 2x + 5 and g(x) = x^2 + x, Describe (i) f+g (ii) f-g (iii) fg (iv) f/g find the domain in each case. Watch Solution
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 (ii) f(x) = √(x – 1) and g(x) = √(x + 1). Watch Solution
If f(x) be defined on [-2, 2] and is given by f (x) = {-1, -2 ≤ x ≤ 0 ; x – 1, 0 less than x ≤ 2 and g(x) = f(|x|) + |f(x)|. Find g(x). Watch Solution
Let f, g be two real functions defined by f(x) = √(x+1) and g(x) = √(9-x^2). Then, describe each of the following functions : (i) f+g (ii) g-f (iii) fg (iv) f/g (v) g/f (vi) 2f – √5g (vii) f^2+7f (viii) 5/g Watch Solution
If f(x) = log(1-x) and g(x) = [x], then determine each of the following functions: (i) f+g (ii) fg (iii) f/g (iv) g/f . Also, find (f+g)(-1), (fg)(0), (f/g)(1/2), (g/f)(1/2) Watch Solution
If f, g, h are real functions defined by f(x) = √(x+1), g(x) = 1/x and h(x) = 2x^2 – 3, then find the values of (2 ƒ + g – h)(1) and (2 ƒ + g – h)(0). Watch Solution
The function f is defined by f(x) = {1 – x, x less than 0 ; 1, x = 0 ; x + 1, x greater than 0. Draw the graph of f(x). Watch Solution
Let f, g:R→R be defined, respectively by f(x) = x + 1, g(x) = 2x – 3. Find ƒ+g, ƒ-g and f/g. Watch Solution
Let f:[0, ∞) → R and g: R→R be defined by f(x) = √x and g(x) = x. Find ƒ+g, ƒ -g, fg and f/g. Watch Solution
Let f(x) = x^2 and g(x) = 2x + 1 be two real functions. Find (f + g)(x), (ƒ – g)(x), (fg)(x) and (f/g)(x). Watch Solution
Chapter 3: Functions – R. D. Sharma Class 11th Maths