Answer:
f(x) + g(x) = [tex]9x^{2} - x - 3[/tex]
f(x) - g(x) = [tex]5x^{2} - 9x + 9[/tex]
g(x) - f(x) = [tex]-5x^{2} + 9x - 9[/tex]
Step-by-step explanation:
[tex]f(x) = 7x^{2} - 5x + 3\ and\ g(x) = 2x^{2} + 4x - 6[/tex]
Case 1:
f(x) + g(x)
= [tex]7x^{2} - 5x + 3 + (2x^{2} + 4x - 6)[/tex]
= [tex]7x^{2} - 5x + 3 + (2x^{2} + 4x - 6)[/tex]
= [tex]9x^{2} - x - 3[/tex]
Case 2:
f(x) - g(x)
= [tex]7x^{2} - 5x + 3 - (2x^{2} + 4x - 6)[/tex]
= [tex]7x^{2} - 5x + 3 - 2x^{2} - 4x + 6[/tex]
= [tex]5x^{2} - 9x + 9[/tex]
Case3:
g(x) - f(x)
= [tex]2x^{2} + 4x - 6 - (7x^{2} - 5x + 3)[/tex]
= [tex]2x^{2} + 4x - 6 - 7x^{2} + 5x - 3[/tex]
= [tex]-5x^{2} + 9x - 9[/tex]
