Ok then, for the following composite function f[g(x)] = [(x^4)+(x^2)]/[1+(x^2)]; given g(x) = 1 - (x^2):
How would you solve for f(x) using "pattern recognition"? I am certain there is an appropriate method to solve using algebra because I remember learning it back in the 8th grade, but as the saying goes, "if you don't use it, you lose it."
Thank you again,
J. Lane
hmm, i believe you are right. i have forgotten the method also. i will try to look it up and get back to you. the "pattern recognition" i talk about is probably using this method without realizing it. i do that sometimes. because i do something over and over, i tend to internalize it and end up doing it "naturally"--forgetting the original method or formula in the process.
here i get
again, recognizing patterns:
note that we have
for , take the negative and add 1, hence you get
for , take the negative and add 2, hence