Question

Find the range of each of the following functions:

(i) f{x) = 2 - 3x, x ∈ R,x>0

(ii) f(x) = x² + 2, x is a real number

(iii) f(x) = x, x is a real number.

Answer 1

(i) Given f(x) = 2 - 3x, x ∈ R,x > 0 

For x > 0, f(x) = 2 – 3x < 2

∴ Range of f = (-∞, 2) 

(ii) Given f(x) = x² + 2, x ∈ R 

For x ∈ R, f(x) = x² + 2 ≥ 2 

Range of f = [2, ∞) 

(iii) Given f(x) = x, x∈ R For r∈ E, f(x) = x ∈ R 

Range of f = R