Notes for Function

Page 1

Inverse Function f^-1 (x)

X Domain f(x) to get Y Range f(x)

Y Domain f^1 (x) to get X Range f^1 (x)

X Domain f(x) is equal to Y Range f^1 (x)

Write equation as y = ...

Switch X and Y

Rearrange to make y subject

Write f^-1(x) place of y

f(x) = 3x - 7

y = 3x - 7

x= 3y - 7

x + 7 = 3y

x+7/3 = y

x+7/3 = f^-1 (x)

f(x) = x^3 - 2

y = x^3 - 2

x = y^3 - 2

x +2 = y^2

3√x+2 = y

f^-1(x) = 3√x+2

Page 2

1. f(x) = -x^2, x ∈ ℝ

Range: (-∞, 0)

2. f(x) = 2x+10, x > 5

Range: (20, +∞)

3. f(x) = 10 - 2x, x<5

Range: (-∞,0)

4. f(x) = -x^2, x>2

Range: (-∞, -4)

5. f(x) = 2x+10 x ≦ 0

Range: (-∞,10]

6. f(x) = 10 - 2x, x < 2

Range: (6, ∞ )

7. f(x) = x^2 + 2, x