For every value of x,the function f(x) = frac | vedclass

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(A) Given the function $f(x) = \frac{1}{5^x} = 5^{-x}$.To determine if the function is increasing or decreasing,we find its derivative with respect to

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Decreasing

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(A) Given the function $f(x) = \frac{1}{5^x} = 5^{-x}$.To determine if the function is increasing or decreasing,we find its derivative with respect to $x$:$f'(x) = \frac{d}{dx}(5^{-x}) = 5^{-x} \cdot \ln(5) \cdot (-1) = -\frac{\ln(5)}{5^x}$.Since $5^x > 0$ for all real $x$ and $\ln(5) \approx 1.609 > 0$,the expression $\frac{\ln(5)}{5^x}$ is always positive.Therefore,$f'(x) = -\frac{\ln(5)}{5^x} Since the derivative $f'(x)$ is negative for all values of $x$,the function $f(x)$ is a strictly decreasing function for all $x$.

For every value of $x$,the function $f(x) = \frac{1}{5^x}$ is:

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