Question

3^2 - 2x + 4 and g(x) = 5x^2 + 6x - 8 find f-g(x)

Answer 1

For the given functions f(x) and g(x)
`(f-g)(x) = -2x^(2)  - 8x +12`

Explanation:

Here, the given function are:

`f(x)  = 3x^(2)  - 2x+ 4\\g(x) = 5x^(2)  + 6x -8`

Now, simplifying for (f-g)(x) = f(x) - g(x):

`f(x) - g(x)  = (3x^(2)  - 2x+ 4) - (5x^(2)  + 6x -8)`

`= 3x^(2)  - 2x+ 4- 5x^(2)  - 6x +8`

Doing operation on LIKE TERMS, we get

f(x) - g(x) =
`( 3x^(2)- 5x^(2))   + (-2x - 6x)  +( 4 +8) = -2x^(2)  - 8x + 12`

Hence, for the given functions f(x) and g(x)
`(f-g)(x) = -2x^(2)  - 8x +12`