Given f (x) = 7x + 8 and g (x) = 9x + 4

Question

. Given f (x) = 7x + 8 and g (x) = 9x + 4  

a.      Find  (f + g) (x) 

b.     Find (f * g) (x) 

c.    Find f ( g(x) )

Answer 1

For a), you simply add the expressions given for f(x) and g(x)

For b), you multiply the same 2 expressions

For c), replace the independent variable in f(x) with the expression for g(x), So:

f ( g (x) ) = 7 * (9x + 4) + 8

= 63x + 28 + 8

= 63x + 36

Adding expressions:

Simply add up the like terms. eg: (2x + 3) + (4x + 5) = 6x + 8

Multiplying expressions:

Multiply one expression by each term of the other. Then collect the like terms and simplify.

Using the same example expressions as above:

(2x + 3) * (4x + 5) = 2x(4x + 5) + 3(4x + 5)

expand:

8x² + 10x + 12x + 15

simplify:

8x² + 22x + 15