For what values of x is the function f(x) = x | vedclass

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(A) Given the function $f(x) = x - \log x$.To find the interval where the function is strictly decreasing,we calculate the derivative $f'(x)$.$f'(x) =

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$x \in (0, 1)$

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(A) Given the function $f(x) = x - \log x$.To find the interval where the function is strictly decreasing,we calculate the derivative $f'(x)$.$f'(x) = \frac{d}{dx}(x - \log x) = 1 - \frac{1}{x}$.For the function to be strictly decreasing,we must have $f'(x) $1 - \frac{1}{x} $\frac{x - 1}{x} Since the domain of $\log x$ is $x > 0$,the denominator $x$ is always positive.Therefore,for the fraction to be negative,the numerator must be negative: $x - 1 Combining this with the domain $x > 0$,we get $x \in (0, 1)$.

For what values of $x$ is the function $f(x) = x - \log x$ strictly decreasing?

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