Question

100 POINTS

Answer 1

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).

What are Quadratic Functions?

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.

How do we solve the problem above?

To solve the problem f(4x - 3) ≥ f(2 - x^2), Df = (-8 , 4), we:

• Rewrite
• Collect like terms
• Expand
• Factorize, then
• Solve for x.

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