Chapter 2: Relations and Functions

Q1. Find the domain and range of f(x) = √(x-2).

Solution

Domain: x - 2 ≥ 0 ⇒ x ≥ 2, i.e., [2, ∞)
Range: [0, ∞)

Q2. Check if f(x) = x² is one-one from R to R.

Solution

f(1) = f(-1) = 1 but 1 ≠ -1. Not one-one since different inputs give same output.

Q3. Let f(x) = 2x + 3. Find f(f(x)).

Solution

f(f(x)) = f(2x+3) = 2(2x+3) + 3 = 4x + 9

Q4. Find gof if f(x) = x+1 and g(x) = x².

Solution

gof(x) = g(f(x)) = g(x+1) = (x+1)² = x² + 2x + 1