Answer
given,
f(x) = x² g(x) = x + 3
a. g( f (5) )
f(5) = 5² = 25
g( f (5) ) = 25 + 3 = 28
b) f (g (5) )
g (5) = 5 + 3 = 8
f (g (5) ) = 8² = 64
c) f ( g(x) )
g (x) = x + 3
f (g (x) ) = (x + 3)² = x² + 6 x + 9
d) g ( f(x) )
f (x) = x²
g ( f(x) ) = x² + 3
e) g (f(√x + 3))
f (√x + 3) = (√x + 3)²
g (f(√x + 3)) = (√x + 3)² + 3
Answer:
See Below
Step-by-step explanation:
Given f(x) = x2, g(x) = x + 3
a. g(f(5)) = g(5^2) = g(25) = 25 + 3 = 28
b. f(g(5)) = f(5+3) = f(8) = 8^2 = 64
c. f(g(x)) = f(x+3) = (x+3)^2 = (x+3)(x+3) = x^2 + 18x + 9
d. g(f(x)) = g(x^2) = x^3 +3x^2
e. g (f(√x + 3)) = g((√x + 3)^2) = (√x + 3)(√x + 3) = x + 3√x + 3√x + 9 =
x + 6√x +9
