1. 
Given the function f (x) = 5x + 4, find f (2m).
Solution: Substitute 2m into the function in place of x. f (2m) = 5(2m) + 4 = 10m + 4.
Using parentheses will avoid problems.
Notice that the answer is an algebraic expression, not a numeric value.

2. 
Given f (x) = 3x^{2} + 2x  3, find f (2a  5).
Solution: Parentheses are a MUST is this problem!
Be careful  more algebra work is needed here.
f (2a  5) = 3(2a  5)^{2} + 2(2a  5)  3
= 3(4a^{2}  20a + 25) + 4a  10  3
= 12a^{2}  60a + 75 + 4a  10  3
=
12a^{2}  56a + 62

3. 
Given g ( a) = 9  a^{2} and h ( a) = a  3, express:
a) g (a) + h (a) 
b) g (a)  h (a) 
c) g (a) • h (a) 
d) , g(a) ≠ 0 
Solution:
a) g (a) + h (a) = (9  a^{2}) + (a  3)
= a^{2} + a + 6 
b) g (a)  h (a) = (9  a^{2})  (a  3)
= a^{2}  a + 12 
c) g (a) • h (a) = (9  a^{2}) • (a  3)
= a^{3} + 3a^{2} + 9a  27 
d)
a ≠ 3; a ≠ 3 

4. 
Given , express .
Solution: Warm up your algebraic fraction skills!

5. 
Given f (x) = x^{2}  x  4. Find f (x + h).
Solution: Be careful to replace the x with (x + h). Use parentheses!!!!
(x+h)^{2}  (x+h)  4
x^{2} + 2xh + h^{2}  x  h  4



6. 
Given g(x) = x^{2} + 1 and h(x) = 5  x. Express 3•g(5  x)  2•h(x^{2})
Solution: Remember to use parentheses!
3g(5  x)  2h(x^{2}) = 3((5  x)^{2} + 1)  2(5  x^{2}) = 3(x^{2}  10x + 25 + 1)  2(5  x^{2})
= 3x^{2}  30x + 78  10 + 2x^{2} = 5x^{2}  30x + 68 
7. 
Solution: FYI: This new expression is called the "difference quotient" or average rate of change.
