Question

Suppose that the functions g and h are defined as follows.g(x) = x-8h(x) = (x+4)(x+5)(a) Find(-3).h(b) Find all values that are NOT in the domain of8hIf there is more than one value, separate them with commas.

Answer 1

The given functions are

g(x) = x - 8

h(x) = (x + 4)(x + 5)

To find (g/h)x, we would divide g(x) by h(x)

Thus,

g(x)/h(x) = (x - 8)/(x + 4)(x + 5)

To find (g/h)(-3), we would substitute x = - 3 into (x - 8)/(x + 4)(x + 5). Thus, we have

(g/h)(-3) = (- 3 - 8)/(- 3 + 4)(- 3 + 5) = - 11 * 1/2

(g/h)(-3) = - 11/2

All values that are not in the domain are all values of x that does not satisfy the expression. If we put x = - 4 or x = - 5 in the denominator, the denominator would be zero and this makes the expression undefined. these values do not satisfy the g/h

Thus, the values are x = - 4 and x = - 5is