Answer:
f(x) ⇒ Graph C
g(x) ⇒ Graph D
h(x) ⇒ Graph A
j(x) ⇒ Graph E
Explanation:
* Lets revise the quadratic function and its inverse
- The quadratic function if f(x) = x², its vertex is the origin
- To find its inverse, switch x and y and solve for y
∵ y = x² ⇒ switch x and y
∴ x = y² ⇒ solve for y
∴ y = ± √x
- If y = √x , then the graph is up the x-axis
- If y = -√x , the graph is down the x-axis
∴ The inverse function is y = √x
* Now lets solve the problem
- All the figure are the inverses of the quadratic function y = x²
∵ f(x) = √(x - 1)
# x - 1 means the graph move to the right 1 unit
∴ Its vertex is (1 , 0)
* The graph of f(x) = √(x - 1) is graph C
∵ g(x) = -√x
# The sign (-) means the graph reflected about the x-axis
∴ Its vertex is (0 , 0) but the graph under the x-axis
* The graph of g(x) = -√x is graph D
∵ h(x) = √x
∴ Its vertex is (0 , 0)
- It is the inverse of y = x² , the graph up to the x-axis
* The graph of h(x) = √x is graph A
∵ j(x) = -√(x - 1)
# x - 1 means the graph move to the right 1 unit
# The sign (-) means the graph reflected about the x-axis
∴ Its vertex is (1 , 0) , the graph down the x-axis
* The graph of j(x) = -√(x - 1) is graph E