The domain of y = log10 \(\big(\sqrt{7-x}+\sqrt{x-3}\big)\) is(a) R�

1.	The domain of y = log10 \(\big(\sqrt{7-x}+\sqrt{x-3}\big)\) is(a) R (b) R – {0} (c) [7, ∞) (d) (3, 7)
Answer» Answer: (d) (3, 7) The function f will be defined if \(\big(\sqrt{7-x} +\sqrt{x-3}\big)\) > 0 i.e., 7 – x > 0 and x – 3 > 0 ⇒ 7 > x and x > 3 ⇒ 3 < x < 7 ∴ Domain of the given function is (3, 7).

The domain of y = log10 \(\big(\sqrt{7-x}+\sqrt{x-3}\big)\) is(a) R (b) R – {0} (c) [7, ∞) (d) (3, 7)

Answer»

Answer: (d) (3, 7)

The function f will be defined if

\(\big(\sqrt{7-x} +\sqrt{x-3}\big)\) > 0

i.e., 7 – x > 0 and x – 3 > 0

⇒ 7 > x and x > 3

⇒ 3 < x < 7

∴ Domain of the given function is (3, 7).