Function Questions

Question

1) Given h(x) = x - 4

g(x) = x² - 6x Find (h + g)(x)

2) Given g(x) = 4x - 4

f(x) = x² - 2x Find (g * f)(n)

3) Given h(n) = 4n - 2

g(n) = -2n + 1 Find (h° g)(n)

Answer 1

1) Just add the two functions: (h + g)(x) = h(x) + g(x) = (x - 4) + (x² - 6x) = x² - 5x - 4

2) Just multiply the two functions: (g * f)(x) = g(x) * h(x) = (4x - 4)(x² - 2x) = (using the FOIL method) 4x³ - 12x² + 8x but the question wants (g * f)(n) so we plug in n for x to get: 4n³ - 12n² + 8n

3) Take function g(n) and plug it into function h(n) wherever you see an n: (h° g)(n) = h(g(x)) = 4(-2n + 1) - 2 = -8n +2