Find the domain of \(\sqrt{x} +\sqrt{3x-2}\)

1.	Find the domain of \(\sqrt{x} +\sqrt{3x-2}\)
Answer» Let f (x) = \(\sqrt{x}\) and g(x) = \(\sqrt{3x-2}\) Let the domain of f (x) be A and that of g(x) be B Then, domain of f (x) = A = [0, ∞] (∵ \(\sqrt{x}\) is defined when x > 0 ) domain of g(x) = B = (\(\frac{2}{3}, \) ∞ ) (∵ \(\sqrt{3x-2}\) is defined when 3x-2 ≥ 0 ⇒ x ≥ \(\frac{2}{3}\) ) ∴ Domain of \(\sqrt{x}\) + \(\sqrt{3x-2}\) = A \(\cap\) B = [0, ∞ ) \(\cap\) [\(\frac{2}{3} \) , ∞ ) = [ \(\frac{2}{3} \), ∞)

Answer»

Let f (x) = \(\sqrt{x}\) and g(x) = \(\sqrt{3x-2}\)

Let the domain of f (x) be A and that of g(x) be B

Then, domain of f (x) = A = [0, ∞] (∵ \(\sqrt{x}\) is defined when x > 0 )

domain of g(x) = B = (\(\frac{2}{3}, \) ∞ ) (∵ \(\sqrt{3x-2}\) is defined when 3x-2 ≥ 0 ⇒ x ≥ \(\frac{2}{3}\) )

∴ Domain of \(\sqrt{x}\) + \(\sqrt{3x-2}\) = A \(\cap\) B = [0, ∞ ) \(\cap\) [\(\frac{2}{3} \) , ∞ )

= [ \(\frac{2}{3} \), ∞)

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