Let A = {x ∈ R, x ≠ 0, – 4 ≤ x ≤ 4) and f : A → R defined by f(x) = |x| / x for x ∈ A. Then the range of f is

Question

Let A = {x ∈ R, x ≠ 0, – 4 ≤ x ≤ 4) and f : A → R defined by\(f(x) = \frac{|x|}{x}\) for x ∈ A. Then the range of f is 

(a) {1, – 1} 

(b) {x : 0 ≤ x ≤ 1} 

(c) {1} 

(d) {x : – 4 ≤ x ≤ 0}

Answer 1

Answer : (a) {1, – 1} 

∵ x ∈ [– 4, 4] 

f (x) = \(\frac{|x|}{x} \) = \(\frac{x}{x}\) = 1 if x is + ve

= \(\frac{x}{-x}\) = -1 if x is -ve

∴ Range of f = {– 1, 1}.