Answer:
The missing words
# x ⇒ # y ⇒ # 4 ⇒ # 0
Step-by-step explanation:
* Lets revise how to find the inverse function
- At first write the function as y = f(x)
- Then switch x and y
- Then solve for y
- The domain of f(x) will be the range of f^-1(x)
- The range of f(x) will be the domain of f^-1(x)
* Now lets solve the problem
∵ f(x) = √(x - 4)
∴ y = √(x - 4) ⇒ switch x and y
∴ x = √(y - 4) ⇒ square the two sides
∴ x² = [√(y - 4)]² ⇒ cancel the root by squaring
∴ x² = y - 4 ⇒ add 4 to the both sides
∴ y = x² + 4
∴ f^-1(x) = x² + 4
* To find the domain of the inverse, find the range of the function
∵ The domain of f(x) is ⇒ x - 4 ≥ 0 (no negative value under√)
∴ the domain is x ≥ 4
- Substitute this value in the function to find the range
∵ x = 4
∴ y = √(4 - 4) = 0
∴ y ≥ 0
- The range of f(x) is y ≥ 0
∴ The domain of the inverse f^-1(x) is x ≥ 0
- The missing words
# x
# y
# 4
# 0
