Question

If f(x)=6x²-4 and g(x)=2x+2, find (f-g)(x)

Answer 1

`(f-g)(x)=6x^(2)-2x-6`

Explanation:

1) Given two functions f(x) and g(x) we can operate them like this:

`f(x)+g(x)=(f+g)(x)\\f(x)-g(x)=(f-g)(x)\\f(x)*g(x)=(f*g)(x)\\f(x):g(x)=(f(x))/(g(x))`

In this question the point is subtracting them, so:

2)

`}\\\\f(x)=6x^(2)-4\, \:\:g(x)=2x+2\Rightarrow (f-g)(x)=6x^(2)-4-(2x+2)\Rightarrow (f-g)(x)=6x^(2)-4-2x-2\Rightarrow (f-g)(x)=6x^(2)-2x-6`

This function has a Domain, as a polynomial function:

`D=\left ( -\infty, +\right )`

And an Range =

`R=[(-37)/(6),\infty)`

Answer 2

6x² - 2x - 6

Explanation:

Note that (f - g)(x) = f(x) - g(x)

f(x) - g(x) = 6x² - 4 - (2x + 2) = 6x² - 4 - 2x - 2 = 6x² - 2x - 6