Question

If f(x) = - x2 + 6x - 1 and g(x) = 3x2 - 4x - 1, find (f- g)(x).

Answer 1

`\fbox{\begin{minipage}{11em}(f - g)(x) = -2x(2x - 5)\end{minipage}}`

Explanation:

Given:

`f(x) = -x^(2) + 6x - 1 \\ g(x) = 3x^(2) - 4x - 1\\`

Solve for:

`(f - g)(x)`

Solution:

Perform the subtraction:

`(f - g)(x) = (-x^(2) + 6x - 1) - (3x^(2) - 4x - 1)`

Eliminate the parenthesis (notice the change in sign of some components):

`(f - g)(x) = -x^(2) + 6x - 1 - 3x^(2) + 4x + 1`

Rearrange the expression:

`(f - g)(x) = (-x^(2) - 3x^(2)) + (6x + 4x) + (1 - 1)`

Simplify the expression:

`(f - g)(x) = -4x^(2) + 10x`

Perform the inverse of associative property:

`(f - g)(x) = -2x(2x - 5)`

Hope this helps!

:)

Answer 2

Explanation:

- 4x² + 10x