Suppose that the functions g and f are defined as follows.

Question

g(x)=-3+2x^2

 

f(x)=9-6x

(a) Find (g/f)(2)
.
(b) Find all values that are NOT in the domain of g/f
.
If there is more than one value, separate them with commas.

(a) Find 

gf2

.
(b) Find all values that are NOT in the domain of 

gf

.
If there is more than one value, separate them with commas.

 

 

Answer 1

g(x)=-3+2x²
f(x)=9-6x

(a) Find (g/f)(2)

g(x)/f(x)=(9-6x)/(2x²-3).

(g/f)(2)=(9-6*2)/(2*2²-3)=-3/5

x=-√3/2 and x=√3/2 are not in domain.

Domail: x∈(-∞, -√3/2)∪(-√3/2, √3/2)∪(√3/2, +∞).

(gf)(2)  is similar