g(x) = f(f) = 1/(1-f) = 1/(1-(1/(1-x)) = 1 - 1/x
h(x) = f(g) = 1/(1-g) = 1/(1-(1 - 1/x)) = x
But, as you say, watch for places where f is undefined. I'm sure you can figure those out.
f(x) =
1/(1−x) is given. From this we produce two new functions:
g(x) = f(f(x)) and h(x) = f(g(x)).
(a) For which values of x is f(x) undefined? (b) Find a formula for g(x), and simplify it. (c) For which values of x is g(x) undefined? (d) Find a formula for h(x), and simplify it. (e) For which values of x is h(x) undefined?
(Hint: Be careful, because there is a trap here. If a value of x won’t work for f, then it also won’t work for g, because you need to compute f before you compute g!)
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sorry but I don't get the part that I should watch for places where f is undefined. I tried to get the value of x that is f(x) undefined and I got x=1
1 answer