Let f(x) = 5x − 6. Simplify each of the following expressions. f(a) =

f(a + h) =

f(a + h) − f(a) = (Make sure to expand and combine like terms.)

f(a + h) − f(a)/h = (Make sure to cancel out the factor of h in the denominator.)

Explanation:

in each of the following substitute x with the variables in the bracket.

f(a) = 5x - 6

= 5a - 6

f(a+h) = 5 (a + h) - 6

= 5a + 5h - 6

f(a+h) - f(a) = (5a + 5h - 6) - (5a - 6)

= 5a + 5h - 6 - 5a + 6

= 5h

(as the 5a's and 6's cancel each other out.)

f(a+h) - f(a)/h = 5a + 5h - 6 - ((5a - 6)÷h)

take l.c.m

= (5ah + 5h^2 - 6h - 5a + 6)

h