2a) The value of h(g2)) is 2
b) The value of f(h(x)) is 5x² + 10
3a) The value of f(g(2)) is -1.5
b) The value of g(f(5) is 2.
How the values of the composite functions are determined.
2 given f(x) = 5x, h(x) = x² + 2 and g(x) = x-4
a) h(g2))
g(2) = 2² + 2
= 4+2 = 6
then h(6) = 6-4 =2
b) f(h(x))
Substitute h(x) into f(x) and simplify
f(h(x)) = 5(x² + 2)
= 5x² + 10
3) From the graphs
a) To find f(g(2))
g(2) = 7, the value of g(x) when x = 2
then,
f(7) = -1.5, when x = 7 from the graph of f(x) it coincide with last line at y = -1.5
b) g(f(5)
f(5) = 0, that x = 5, the graph intersect the x axis therefore f(x) = 0
then,
g(0) = 2, at x = 0 the table of g(x) is 0.