three or more non-identity functions

Question

write the function f(x) = √(x^3+6)/(x^3-9), as a composition of three non-identity functions

Answer 1

Hi Molly,

They’re asking us to rewrite the function in three pieces, so we’ll let:

w(x) = x³ - 9

v(x) = x³ + 6

u(x) = √x

It is easy to see that v(x)/w(x) = the fraction that’s inside the square root of the original function, so we can write:

f(x) = u[v(x)/w(x)]

Please let me know if I can be more helpful, thanks!

Joe