Let f : R → R be defined as f(x) = x4 . Choose the correct answer.

1.	Let f : R → R be defined as f(x) = x4 . Choose the correct answer. (A) f is one-one onto (B) f is many-one onto (c) f is one-one but not onto (D) f is neither one-one nor onto.
Answer» Answer is (D) f (x,) = f (x₂) ⇒ x₁⁴ = x₂⁴ = x₁⁴ = x₂⁴= 0 = (x₁ – x₂) (x₁ + x₂) (x₁² = x₂²) x₁ = x₂ or x₁ = – x₂ ∴ f is not one-one f(x) = x⁴ ≥ o ∀ x ∈ R Range of f = [0, ∞) ∈ R

Let f : R → R be defined as f(x) = x4 . Choose the correct answer. (A) f is one-one onto (B) f is many-one onto (c) f is one-one but not onto (D) f is neither one-one nor onto.

Answer»

Answer is (D)

f (x,) = f (x₂) ⇒ x₁⁴ = x₂⁴

= x₁⁴ = x₂⁴= 0

= (x₁ – x₂) (x₁ + x₂) (x₁² = x₂²)

x₁ = x₂ or x₁ = – x₂

∴ f is not one-one

f(x) = x⁴ ≥ o ∀ x ∈ R

Range of f = [0, ∞) ∈ R