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 squa

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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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