1) The domain for f (x) and g (x) is the set of all real numbers. Let f (x) = 2x-3 and g (x) = 3x+8. Find f (x) multiplied by g (x). 2) The domain for f (x) and g (x) is the set of all real numbers. Let f (x) = x^2+x-20 and g (x) = x+5. Find f (x) / g (x) <- - (this is a fraction.) 3) Evaluate the piecewise function at x=-3 and x-11. 4) Find the inverse of the function. F (x) = 3x+7.

1) 6x^2+7x-24

2) x-4

3) f (-3) = -14 g (-3) = 2 f (-3) / g (-3) = -7 and p (-3) = -3-4=-7

f (-11) = 90 g (-11) = -6 f (-11) / g (-11) = -15 and p (-11) = -11-4=-15

4) f' (x) = (x-7) / 3

Step-by-step explanation:

1) f (x) = 2x-3 g (x) = 3x+8

f (x) * g (x) = m (x) = (2x-3) (3x+8) = 6x^2+16x-9x-24=6x^2+7x-24

2) f (x) = x^2+x-20 g (x) = x+5

f (x) / g (x) = p (x) = (x^2+x-20) / (x+5) = > by finding the roots of f (x) we obtain =

(x-4) (x+5) / (x+5) - -->f (x) / g (x) = p (x) = (x-4)

3) f (-3) = -14 g (-3) = 2 f (-3) / g (-3) = -7 and p (-3) = -3-4=-7

f (-11) = 90 g (-11) = -6 f (-11) / g (-11) = -15 and p (-11) = -11-4=-15

4) If a function f (x) is mapping x to y, then the inverse function of f (x) maps y back x

y=3x+7

(y-7) / 3=x=--> f' (x) = (x-7) / 3