Question

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

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.

Answer 1

Following are the solution to the given question:

Explanation:

Given:

`\to g(x)= -3+2x^2 \\\\\to f(x)=9-6x`

Calculating the value of
`((g)/(f))(2)`:

`\to ((g)/(f)) (2)= ((g(x))/(f(x))) * (2)`

`=(2x^2-3)/(9-6x) * 2\\\\=(2\cdot 2^2-3)/(3(3-2\cdot 2)) \\\\=(2\cdot 4-3)/(3(-1))\\\\ =(8-3)/(-3)\\\\ =(5)/(-3)\\\\ = - (5)/(3)\\\\`

x=
`- (√(3))/(2)` and x=
`(√(3))/(2)` are not in the domain.

Domain:
`x \belong (- \infty, -(√(3))/(2))\cup (- (√(3))/(2), (√(3))/(2) )\cup ((√(3))/(2), \infty)`