\( y=\log _{10}(-1+|x-1 / 2|) \)

Question

doubt in 9

Answer 1

y = log₁₀(-1 + 1 + |x - 1/2|)

To defined log x, we have

-1 + |x - 1/2| > 0

⇒ |x - 1/2| > 1

⇒ x - 1/2 > 1 or x - 1/2 < - 1

⇒ x > 3/2 or x < -1/2

⇒ x \(\in\) (\(-\infty, \frac{-1}2\)) U (3/2, \(\infty\))

Domain of y is (-\(\infty\), -1/2) U (3/2, \(\infty\))