The domain of the function is f (x) = 1 / (log10 x)

Question

The domain of the function is f (x) = \(\frac{1}{log_{10} x}\) 

(a) R 

(b) R⁺ ∪ {0} 

(c) R⁺ – {1} 

(d) R – {0}

Answer 1

Answer : (c) = R⁺ – {1} 

\(\frac{1}{log_{10} x} =log_x 10\)  which is defined only when x > 0, x ≠ 1 

∴ Domain of the given function is the set of all non-zero positive real number except 1, i.e., R⁺ – {1}.

Note : Similarly the domain of \(\frac{1}{log|x|}\) is R – {0, 1, – 1}