For every value of x in [1, 3],the function f | vedclass

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(C) Given function is $f(x) = \frac{1}{8^x} = 8^{-x}$.To determine the nature of the function,we find its derivative with respect to $x$:$f'(x) = \fra

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decreasing.

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(C) Given function is $f(x) = \frac{1}{8^x} = 8^{-x}$.To determine the nature of the function,we find its derivative with respect to $x$:$f'(x) = \frac{d}{dx}(8^{-x}) = 8^{-x} \cdot \ln(8) \cdot (-1)$.$f'(x) = -\frac{\ln(8)}{8^x}$.Since $8^x > 0$ for all $x \in [1, 3]$ and $\ln(8) > 0$,the expression $f'(x) = -\frac{\ln(8)}{8^x}$ is always negative for all $x \in [1, 3]$.Since $f'(x) < 0$ for all $x \in [1, 3]$,the function $f(x)$ is a decreasing function on the interval $[1, 3]$.

For every value of $x \in [1, 3]$,the function $f(x) = \frac{1}{8^x}$ is

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