Question
Construct the following composite functions and specify the domain of each.(a) $f \circ f(x)$(b) $f \circ g(x)$(c) $g \circ f(x)$(d) $g \circ g(x)$$$f(x)=1 /(1-x), \quad g(x)=\sqrt{x-1}$$
Step 1
So we have $f(f(x)) = f(1/(1-x)) = 1/(1 - 1/(1-x))$. Simplifying this, we get $f(f(x)) = (x-1) / x$. The domain for this function is all real numbers except 0 and 1, because the denominator cannot be zero. Show more…
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