Answer:
f[g(3)] = 100
g[f(5)] = 138
g{f[g(-4)]} = -982
Step-by-step explanation:
f(x) = 4x - 3
g(x) = 8x + 2
a. f[g(3)]
First find g(3) by putting x = 3 in g(x) function
g(3) = 8(3) + 2 = 24 +2 = 26
now put this g(3) = 26 as x in f(x)
f(g(3)) = f(26) = 4(26) - 4 = 104 - 4 = 100
b. g[f(5)]
First lets find f(5)
f(x) = 4x - 3
put x = 5 above
f(5) = 4(5) - 3 = 20 - 3 = 17
put this f(5) = 17 as x in g(x)
g(f(5)) = g(17) = 8(17) + 2 = 138
c.g{f[g(-4)]}
First lets solve the inner most function
g(-4) = 8(-4) +2 = -30
put g(-4) = -30 in f(x) to find f(g(-4))
f(g(-4)) = f(-30) = 4(-30) - 3 = -123
put f(g(-4)) = -123 as x in g(x) to find our complete result
g{f[g(-4)]} = g(-123) = 8(-123) + 2 = -982
