Find $$ (f \circ g)(x) $$ and $$ (g \circ f)(x) $$ for the pair of functions and give the domains. $$ f(x)=\frac{2}{x^{2}}, g(x)=8-x $$ Find $$ (f \circ g)(x) $$. $$ (f \circ g)(x)=\square $$

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$$ (f \circ g)(x) = \frac{2}{(8 - x)^{2}} $$, domain: all real numbers except $$ x = 8 $$. To find $$ (f \circ g)(x) $$, we need to first find $$ f(g(x)) $$. Given: $$ f(x) = \frac{2}{x^{2}} $$ $$ g(x) = 8 - x $$ To find $$ f(g(x)) $$, we substitute $$ g(x) $$ into $$ f(x) $$: $$ f(g(x)) = f(8 - x) $$ Now, we substitute $$ 8 - x $$ into $$ f(x) $$: $$ f(8 - x) = \frac{2}{(8 - x)^{2}} $$ Therefore, $$ (f \circ g)(x) = \frac{2}{(8 - x)^{2}} $$. The domain of $$ (f \circ g)(x) $$ is the set of all real numbers except for the values that make the denominator zero. In this case, the denominator is $$ (8 - x)^{2} $$, which is zero when $$ x = 8 $$. So, the domain of $$ (f \circ g)(x) $$ is all real numbers except $$ x = 8 $$. Therefore, $$ (f \circ g)(x) = \frac{2}{(8 - x)^{2}} $$ and the domain is all real numbers except $$ x = 8 $$.

Find \( (f \circ g)(x) \) and \( (g \circ f)(x) \) for the pair of functions and give the domains. \( f(x)=\frac{2}{x^{2}}, g(x)=8-x \) Find \( (f \circ g)(x) \). \( (f \circ g)(x)=\square \)

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Find \( (f \circ g)(x) \) and \( (g \circ f)(x) \) for the pair of functions and give the domains. \( f(x)=\frac{2}{x^{2}}, g(x)=8-x \) Find \( (f \circ g)(x) \). \( (f \circ g)(x)=\square \)

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