Question

What is the y value when f(x)=g(x)

f(x)= 2x^3+2x-3
g(x)= -0.5|x-4|

Answer 1

x = 0.5 because when we plug x = 1.056525 into the original equation, it is not true.

Explanation:

1.) f(x) = 2x^3 + 2x - 3 and g(x) = - 0.5 |x - 4|

2.) 2x^3 + 2x - 3 = - 0.5 |x - 4|

3.) 2x^3 + 2x - 3 = - 0.5(x - 4)

• 2x^3 + 2x - 3 = - 0.5x + 2
• 2x^3 + 2x - 3 + 0.5x - 2 = 0
• 2x^3 + 2.5x - 5 = 0
• x = 1.056525

4.) 2x^3 + 2x - 3 = - 0.5 x - (x - 4)

• 2x^3 + 2x - 3 = - (- 0.5(x -4))
• 2x^3 + 2x - 3 = 0.5x - 2
• 2x^3 + 2x - 3 - 0.5x + 2 = 0
• 2x^3 + 1.5x - 1 = 0
• x = 0.5

5.) x = 0.5, 1.056525

6.) When x = 1.056525, the original equation 2x^3 + 2x - 3 = - 0.5 |x - 4| does not hold true. We will drop x = 1.056525 from the solution set.

7.) x = 0.5