Find the range of each of the following functions:(i) f{x) = 2 - 3x, x

1.	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» (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

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»

(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