Suppose that the functions g and h are defined as follows

Question

g(x)=x+9

h(x)=(x+2)(x-5)

(a) find (g/h)(-6)

(b) find all the values that are NOT in the domain of g/h

if there is more than one value, separate them with commas

(a) (g/h)(-6)=

(b) value(s) that are NOT in the domain of g/h :

Answer 1

f = g/h g(x) = x+9 h(x) =(x+2)(x-5)

f(-6) = (g/h)(-6) = g(-6)/h(-6)

= (-6 + 9) / [ (-6+2)(-6-5) ]

f(-6) = (3)/[ (-4)(-11) ] = 3/44

Because one cannot divide by zero, with h in the denomiator, whenever x+2 = 0 or x - 5 = 0

there will be a problem. So we solve these and find that x canNOT be -2, nor can it be 5. So part

b answer would be x≠-2,5 or the values of x that are NOT in the domain are -2,5