Advanced functions/precalculus
posted by Diane on .
1. Given f(x)=x^2 and g(x)=x+2, determine in standard form:
a) g(f(x))
b) when f(g(x))=g(f(x))
2. If f = {(10, 1), (1, 1), (10, 0), (11, 7)} and g = {(1, 1), (0, 10), (1, 10), (7, 11)} for how many values of x is f x g defined? Explain
3. Given f(x) = 2x + 3 and g(x) = 3x + 4, x ε R, use the sketches of both functions to graph (fg)(x) on the same graph. Show your work.

#1.
g(f) = f+2 = x^2+2
f(g) = g^2 = (x+2)^2
so, when do we have
x^2+2 = (x+2)^2
?
#2.
f and g are both defined only on {1}
#3.
visit wolframalpha.com
(fg)(x) = 6x^2+x+12