Thread: function composition

"If f(x) = 4x, g(x) = 2x – 1 and h(x) = x2 + 1, find each value."
a. h[g(4)]

b. f[f(-3)]

c. g[h(-1/2)]

d. [f ○ (h ○ g)](3)

I don't really know where to start with this question so any help on it would really be appreciated.

a) first calculate g(4) (replacing x by 4 in the expression of g(x)), and then calculate the of that value.
idem for b) c)

d) , so what is ? and use the same reasoning as in a)

not factoring ... this is function composition.

a. h[g(4)]

first calculate g(4) ...

g(x) = 2x - 1

g(4) = 2(4) - 1 = 7

h[g(4)] = h(7) = (7)^2 + 1 = 50

you do b and c.

d. [f ○ (h ○ g)](3) = f[h[g(3)]]

start by evaluating g(3) , then h[g(3)], then f[h[g(3)]] ... work inside out.