Composition of Functions & Domain

f(g(x))

100

f(x) = x²

g(x) = x + 2

(x + 2)²

200

f(x) = 1/x

g(x) = x²

1/x²

300

f(x) = x³

g(x) = x^1/3

x

400

f(x) = x⁴ + 5

g(x) = 1/x²

(1/x²)⁴ + 5

500

f(x) = x² + x + 2

g(x) = x - 2

(x - 2)² + x

f o g o f

100

f(x) = x²

g(x) = x + 1

(x² + 1)²

200

f(x) = x^1/2 

g(x) = x⁴

x

300

f(x) = x + 3

g(x) = x - 3

x + 3

400

f(x) = x² + 2x

g(x) = 4x

(4x² + 8x)² + 2(4x² + 8x)

500

f(x) = x³ + x

g(x) = x² + 4x

((x³ + x)² + 4(x³ + x))³ + (x³ + x)² + 4(x³ + x)

Domain (Denominators)

100

f(x) = 1/x

(-∞ , 0) U (0, ∞)

200

1/(x-1)

(-∞ , 1) U (1, ∞)

300

2/(2x + 1)

(-∞ , -1/2) U (-1/2, ∞)

400

x / 4x - 8

(-∞ , 2) U (2, ∞)

500

1/(x² + 2x - 3)

(-∞ , -3) U (-3,1) U (1,∞)

Domain (Radicals)

100

√(x)

[0, ∞)

200

√(x-1)

[1, ∞ )

300

√(x+2)

[-2, ∞)

400

√(x²-4)

(-∞ , -4) U (4, ∞)

500

√(x²)

(-∞ , ∞ )

Wild Card (any category)

100

Find the domain of √(x)

[0,∞)

200

find h(g(b)): h(b) = b² -1, g(b) = b+1

(b+1)² -1

300

Calculate g(f(g(x))): g(x) = x+2, f(x) = 5x

5x + 12

400

Find f(g(c)): f(c) = c + x, g(c) = c(a)

c(a) + x

500

Find the domain of √ (x+1) / x

[-1,0) U (0, ∞)