Question

Suppose -3x²+24x-53<=f(x)<=3x²-24x+43 for all x values near 4 , except possibly at 4 .

Answer 1

To solve the quadratic inequalities, we set the two expressions separately and find the values of x that satisfy them. In this case, the values of x near 4 that satisfy the inequalities are 4 and any number less than 4.

Step-by-step explanation:

The given expression is a quadratic inequality. To solve it, we need to find the values of x that satisfy the inequality. Let's break it down:

• First, we'll set the two quadratic expressions separately:
• -3x² + 24x - 53 <= f(x)
• f(x) <= 3x² - 24x + 43
• We'll solve each expression individually:
• -3x² + 24x - 53 <= f(x)
• f(x) <= 3x² - 24x + 43
• Next, we'll take 4 as the starting point and find the x values near 4 that satisfy the inequalities:
• -3x² + 24x - 53 <= f(x) --> -3(4)² + 24(4) - 53 <= f(4) --> -3(16) + 96 - 53 <= f(4) --> -48 + 96 - 53 <= f(4) --> -5 <= f(4)
• f(x) <= 3x² - 24x + 43 --> f(4) <= 3(4)² - 24(4) + 43 --> f(4) <= 3(16) - 96 + 43 --> f(4) <= 48 - 96 + 43 --> f(4) <= -5
• So, the values of x near 4 that satisfy the inequalities are 4 and any number less than 4.