This solution is arrived at using the principles of Quadratic Functions and Inequalities. It is to be noted that the function increases at (-8, 4).
<h3>What are Quadratic Functions?</h3>
A quadratic function can be defined as that is written in the following way: f(x) = ax2 + bx + c: Where a, b, and c are numbers not equal to zero.
<h3>How do we solve the problem above?</h3>
To solve the problem f(4x - 3) ≥ f(2 - x^2), Df = (-8 , 4), we:
- Rewrite
- Collect like terms
- Expand
- Factorize, then
- Solve for <em>x</em>.
A) 4x - 3 ≥ 2 - x²
Rewrite as: x² + 4x - 2 - 3 ≥ 0
B) Collect the like terms
x² + 4x - 5 ≥ 0
C) Expand to have x² + 5x - x - 5 ≥ 0
D) Factorizing the expression we have
x(x + 5) - 1(x + 5) ≥ 0, from this we Factor away x + 5
(x - 1)(x + 5) ≥ 0
E) Solving for x we obtain: x ≥ 1 or x ≥ -5
This can also be rewritten to read:
-5 ≤ x ≤ 1
Learn more about quadratics and inequalities at:
brainly.com/question/2237134
