EDGE Math 8

Example 2

If $f (x) = x^{2} - 1$ and $g (x) = x + 2,$ determine the following:

1.

(\frac{f}{g}) (- 3)

2.

(f \circ g) (x)

3.

(g \circ f) (- 2)

Solution

1.	$f (- 3) = {(- 3)}^{2} - 1 = 8$ and $g (- 3) = - 3 + 2 = 1$
	$(\frac{f}{g}) (- 3) = \frac{f (- 3)}{g (- 3)} = \frac{8}{- 1} = - 8$

2.	$(f \circ g) (x) = f (g (x))$ $= f (x + 2)$ $= {(x + 2)}^{2} - 1$ $= x^{2} + 4 x + 4 - 1$ $= x^{2} + 4 x + 3$

3.	$(g \circ f) (- 2) = g (f (- 2))$ $= g ({(- 2)}^{2} - 1)$ $= g (3)$ $= 3 + 2$ $= 5$