The domain of the function f (x) = exp\(\sqrt{5x-3-2x^2}\) is:(a) [

1.	The domain of the function f (x) = exp\(\sqrt{5x-3-2x^2}\) is:(a) [ \(\frac{3}{2}\) ∞ )(b) [1, \(\frac{3}{2}\) ](c) [– ∞, 1] (d) (1, \(\frac{3}{2}\))
Answer» Answer : (d) (1, \(\frac{3}{2}\)) Given f (x) = \(exp(\sqrt{5x-3-2x^2}) = exp(\sqrt {-(2x^2-5x+3)})\) For f (x) to be defined – (2x² – 5x + 3) ≥ 0 ⇒ 2x² – 5x + 3 ≤ 0 ⇒ 2x² – 3x – 2x + 3 ≤ 0 ⇒ (2x – 3) (x – 1) ≤ 0 ( ∵ (x-a) (x-b) ≤ 0 ⇒ a ≤ x ≤ b where a < b) ⇒ \(x\leq \frac{3}{2}\) and x ≥ 1 ⇒ 1 ≤ x ≤ \(\frac{3}{2}\)

The domain of the function f (x) = exp\(\sqrt{5x-3-2x^2}\) is:(a) [ \(\frac{3}{2}\) ∞ )(b) [1, \(\frac{3}{2}\) ](c) [– ∞, 1] (d) (1, \(\frac{3}{2}\))

Answer»

Answer : (d) (1, \(\frac{3}{2}\))

Given f (x) = \(exp(\sqrt{5x-3-2x^2}) = exp(\sqrt {-(2x^2-5x+3)})\)

For f (x) to be defined

– (2x² – 5x + 3) ≥ 0

⇒ 2x² – 5x + 3 ≤ 0

⇒ 2x² – 3x – 2x + 3 ≤ 0

⇒ (2x – 3) (x – 1) ≤ 0 ( ∵ (x-a) (x-b) ≤ 0 ⇒ a ≤ x ≤ b where a < b)

⇒ \(x\leq \frac{3}{2}\) and x ≥ 1

⇒ 1 ≤ x ≤ \(\frac{3}{2}\)