Solve this: Question No 4 The domain of the function fx=1-loge1-2x isA - , 1-e2∪12, B - Maths - Relations and Functions

Question

Solve this:

Question No 4
The domain of the function

f x = 1 - log e 1 - 2 x   is A   - ∞ ,   1 - e
2 ∪ 1 2 , ∞ B   [ 1 - e 2 ,   1 2 ) C   1
- e 2 ,   1 2 D   ( 1 - e 2 ,   1 2 ]

Aarushi Mishra · Accepted Answer

fx=1-loge1-2xQunatity inside square root should be non-negative1-loge1-2x≥0loge1-2x≤1Since e>1, by using logarithmic inequality for base >1, logab≤c⇒001>2xx<121-2x≤e2x≥1-ex≥1-e2x∈[1-e2, 12)Domain, x∈[1-e2, 12)

Solve this: Question No. 4 The domain of the function f x = 1 - log e 1 - 2 x is A - ∞ , 1 - e 2 ∪ 1 2 , ∞ B [ 1 - e 2 , 1 2 ) C 1 - e 2 , 1 2 D ( 1 - e 2 , 1 2 ]

Solve this:

Question No. 4
The domain of the function

$f (x) = \sqrt{1 - \log_{e} (1 - 2 x)} is (A) (- \infty, \frac{1 - e}{2}) \cup (\frac{1}{2}, \infty) (B) [\frac{1 - e}{2}, \frac{1}{2}) (C) (\frac{1 - e}{2}, \frac{1}{2}) (D) (\frac{1 - e}{2}, \frac{1}{2}]$