Problem Set 2
1. For the given function, determine each of the quantities stated next to it
a)
f(x) = 5x2 + 7x + 1 f(y); f(x + a); f( f(x) )
f(y) = 5y2 + 7y + 1
f(x+a) = 5(x+a)2 +
7(x+a) + 1
f(f(x)) = 5(f(x))2 + 7f(x) + 1 = 5(5x2 + 7x + 1)2 +
7(5x2 + 7x + 1) + 1 =
b) f(z) =
z3 + 1
f(x);
f( z + h);
f(1/x)
f(x) = x3 + 1
f(z+h) = (z+h)3
+ 1
f(1/x) =
(1/x)3 + 1
=1/x3 +
1
c) f(x) =
2 f(x+h);
f(z) ;
f(3)
f(x+h) = 2
f(z) = 2
f(3) = 2 ( f of everything is 2!)
d) f(x) =
1/x f(2+h); f(3/2); f(1/y)
f(2+h) = 1/(2+h) f(3/2) =
2/3
f(1/y) = y
2. For each function below, state what it’s domain and range are
a)
f(x) = |x|
+ 2
domain: all reals
range: all reals greater than or equal to
2
b)
f(x)
= 3 sin(x)
domain:
all reals
range: all reals between -3 and +3
c)
f(x) = 
domain:
all reals ≥ 6
range: all reals ≥ 9
d)
f(x) = x2 + 4 domain: all
reals
range: all reals
≥ 4