TS EAMCET · Maths · Functions
To set of all real values of \(x\) for which \(f(x)=\log _2\left(2^x-2\right)+\sqrt{1-x}\) is also real is
- A R
- B \((1, \infty)\)
- C \((-\infty, 1]\)
- D \(\phi\)
Answer & Solution
Correct Answer
(D) \(\phi\)
Step-by-step Solution
Detailed explanation
Given function \(f(x)=\log _2\left(2^x-2\right)+\sqrt{1-x}\) It should have real values for any set of values of \(x\). For real \(f(x), \sqrt{1-x}\) must be greater than or equal to 0 and \(\left(2^x-2\right)\) also greater than 0 . So,…
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