The set of all real values of x for which f(x | vedclass

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(D) For the function $f(x) = \log_2(2^x - 2) + \sqrt{1 - x}$ to be defined,both the logarithmic and square root terms must be real. $1$. For the squar

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$\phi$

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(D) For the function $f(x) = \log_2(2^x - 2) + \sqrt{1 - x}$ to be defined,both the logarithmic and square root terms must be real. $1$. For the square root,we require $1 - x \geq 0$,which implies $x \leq 1$. $2$. For the logarithm,we require the argument to be positive: $2^x - 2 > 0$,which implies $2^x > 2^1$,so $x > 1$. Combining these two conditions,we need $x \leq 1$ $AND$ $x > 1$. Since there is no real number $x$ that satisfies both $x \leq 1$ and $x > 1$ simultaneously,the set of such values is the empty set,denoted by $\phi$.

The set of all real values of $x$ for which $f(x) = \log_2(2^x - 2) + \sqrt{1 - x}$ is real is:

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