Question

f,g,h:R ->R,f(x) = 3x + 7,g(x) =x - 4,h(x) =x 2 + 1. Instead of x 2 , you may use: x * x Determine f o g and h o g (evaluate completely and combine like terms).

Answer 1

f(g(x)) = 3x -5

h(g(x)) = x^2 -8x +17

Explanation:

— f(g(x))

f(g(x)) = f(x -4) = 3(x -4) +7 = 3x -12 +7

f(g(x)) = 3x -5

_____

— h(g(x))

h(g(x)) = h(x -4) = (x -4)^2 +1 = x^2 -8x +16 +1

h(g(x)) = x^2 -8x +17