Express the function $$ h(x)=\frac{1}{x-1} $$ in the form $$ f \circ g $$. If $$ g(x)=(x-1) $$, find the function $$ f $$ Your answer is $$ f(x)=\square $$ Question Help: Video Submit Question

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$$ f(x) = \frac{1}{x} $$ To express the function $$ h(x) = \frac{1}{x-1} $$ in the form $$ f \circ g $$, where $$ g(x) = x - 1 $$, we need to find a function $$ f $$ such that: $$ h(x) = f(g(x)) $$ Substituting $$ g(x) $$ into the equation, we have: $$ h(x) = f(x - 1) $$ Since $$ h(x) = \frac{1}{x-1} $$, we can set this equal to $$ f(x - 1) $$: $$ f(x - 1) = \frac{1}{x - 1} $$ To find $$ f $$, we need to express $$ f $$ in terms of its argument. Let $$ u = x - 1 $$. Then, we can rewrite the equation as: $$ f(u) = \frac{1}{u} $$ Thus, we can express $$ f $$ as: $$ f(x) = \frac{1}{x} $$ Therefore, the function $$ f $$ is: $$ \boxed{\frac{1}{x}} $$

Express the function \( h(x)=\frac{1}{x-1} \) in the form \( f \circ g \). If \( g(x)=(x-1) \), find the function \( f \) Your answer is \( f(x)=\square \) Question Help: Video Submit Question

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Express the function \( h(x)=\frac{1}{x-1} \) in the form \( f \circ g \). If \( g(x)=(x-1) \), find the function \( f \) Your answer is \( f(x)=\square \) Question Help: Video Submit Question

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