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

Question

asked Dec 4, 2021 223k views

2 Answers

Geekoverdose · Answer 1 · 2021-12-05T04:00:25+0000

Answer:

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

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!

:)