Question

Let f(x) = x2, g(x) = x + 3.

a. g(f(5))
b. f(g(5))
c. f(g(x))
d. g(f(x))
e. g (f(√x + 3))

Answer 1

See Below

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

Answer 2

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