Functions-Operations, Compositions, & Inverses

Adding & Subtracting Functions

100

(f + g)(x), if f(x) = 4x + 8 and g(x) = 2x -12(f + g)(x)

6x - 4

200

(f + g)(x), if f(x) = x + 2 and g(x) = 2x²

2x² + x + 2

300

The domain of (f - g)(x) = 2x + 20

D: All real numbers

400

(f - g)(x), if f(x) = 2x² + 8 and g(x) = x - 3 AND its domain

2x² - x + 11

D: All real numbers

500

3f(x) + 5g(x), if f(x) = -3x + 2 and g(x) = x/5

-8x + 6

Multiplying & Dividing Functions

100

(f * g)(x), if f(x) = 4x + 8 and g(x) = 2x - 12

8x² - 32x - 96

200

(f * g)(x), if f(x) = x + 2 and g(x) = 2x²

2x³ + 4x²

300

(f/g)(x), if f(x) = 4x + 8 and g(x) = 2x - 12

2x + 4/x - 6

400

(g/f)(x), if f(x) = x + 2 and g(x) = 2x²

2x²/x + 2

500

(f/g)(x), if f(x) = x + 2 and g(x) = 2x² AND its domain

x + 2/2x²

D: All real numbers, except x = 0

Composing Functions

100

g(f(x)), if f(x) = -3x + 2 and g(x) = x/5

-3x + 2/5

200

(f ⁰ g)(x), if f(x) = x - 5 and g(x) = x²

x² - 5

300

(g ⁰ f)(4), if f(x) = x - 2 and g(x) = x²

4

400

f(g(1)), if f(x) = -3x + 2 and g(x) = x/5

7/5

500

(f ⁰ g)(-5), if f(x) = 3x and g(x) =(x + 2)²

27

Inverse Functions

100

The inverse of the relation:

s = {(3, -1), (5, 1), (3, 3), (2, 1), (0, -2)} 

s^-1 = {(-1, 3), (1, 5), (3, 3), (1, 2), (-2, 0)}

200

Inverse of f(x) = x + 2

f^-1(x) = x - 2

300

Inverse of f(x) = 2x - 1/3

f^-1(x) = 1/2x + 1/6

400

The domain and range of g(x) = √3x - 9

D: x ≥ 3

R: y ≥ 0

500

f and g are inverse functions, if f(x) = x² - 49 and 

g(x) = x + 7

No