Hi I'm just wondering how the following would be done.
Lets say I defined f(x) = x^2 if 0< x<0.5 and -x if -0.5 < x < 0.
The graph would simply be a straight line with slope negative one from x = -0.5 to x = 0. For 0 < x <= 0.5 the graph would be a parabola. My question is, how would I find the equation for f(f(x)). That is, f applied to itself.
I'm thinking that the rule for f(f(x)) could be obtained by taking the rule for f(x) and replacing x by x^2 and x by -x in the relevant parts of the rule for f(x). But what would the domain of f(f(x)) be and how would I find it? Would the domain of f(f(x)) be the range of f(x)? I would really appreciated any help with this question.
Ghandi10
Lets say I defined f(x) = x^2 if 0< x<0.5 and -x if -0.5 < x < 0.
The graph would simply be a straight line with slope negative one from x = -0.5 to x = 0. For 0 < x <= 0.5 the graph would be a parabola. My question is, how would I find the equation for f(f(x)). That is, f applied to itself.
I'm thinking that the rule for f(f(x)) could be obtained by taking the rule for f(x) and replacing x by x^2 and x by -x in the relevant parts of the rule for f(x). But what would the domain of f(f(x)) be and how would I find it? Would the domain of f(f(x)) be the range of f(x)? I would really appreciated any help with this question.
Ghandi10
