The domain of the function f (x) = exp √ (5x-3-2x^2) is:

Question

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 1

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 ≤ \(\frac{3}{2}\)