advanced functions/precalculus
posted by Diane on .
1. The function f(x) = (2x + 3)^7 is the composition of two functions, g(x) and h(x). Find at least two different pairs of functions g(x) and h(x) such that f(x) = g(h(x)).
2. Give an example of two functions that satisfy the following conditions:
 one has 2 zeros
 one has no zeros
 the sum of the functions has 1 zero
Show that your functions satisfy the conditions.

g(x) = x^7
h(x) = 2x+3
g(x) = (2x+1)^7
h(x) = x+1
f(x) = x^21
g(x) = x^2+1
(f+g)(x) = 2x^2 (one unique zero, repeated)
f(x) = 3x+x^2
g(x) = 2x^2
(f+g)(x) = 3x+2 (only a single zero)