Respuesta :
Point (0, 1) is on the graph of the inverse function h⁻¹(x).
What is an Inverse Function?
- If f(x) is an original function with output y, then we can get inverse of the original function by putting y in the inverse function to obtain x.
- The domain of original function becomes the range of its inverse function and the range of the original function becomes the domain of its inverse function.
Given: The graph of function y = h(x).
According to the graph, the function is a straight line:
y-intercept is (c) = 2
Consider two points on the graph, y = h(x).
Let (x₁, y₁) = (0, 2) and (x₂, y₂) = (2, -2).
Now, the slope (m) of the function will be calculated as:
⇒ m = (y₂ - y₁) / (x₂ - x₁)
⇒ m = (-2 - 2) / (2 - 0)
⇒ m = -2
Now, with c = 2 and m = -2 the equation of a given line will be calculated as:
The general equation of line is:
⇒ y = mx + c
⇒ y = -2x + 2
∴ y = h(x) = -2x + 2 is the given equation of line.
Now to find the h⁻¹(x), we have to interchange the values of x and y from the function h(x) and then obtain the relation for the general equation of line.
h⁻¹(x) will be calculated as:
⇒ x = -2y + 2
⇒ x - 2 = -2y
⇒ y = (2 - x)/2
∴ y = h⁻¹(x) = (2 - x)/2
Now, we will find which point is on the graph of h⁻¹(x).
Option (A): (2, 4)
put, x = 2 in the equation y = (2 - x)/2
⇒ y = 0
⇒ (2, 0) ≠ (2, 4)
∴ (2, 4) is not the point on h⁻¹(x).
Option (B): (0, 1/2)
put x = 0 in the equation y = (2 - x)/2
⇒ y = 1
⇒ (0, 1) ≠ (0, 1/2)
∴ (0, 1/2) is not the point on h⁻¹(x).
Option (C): (0, 1)
put x = 0 in the equation y = (2 - x)/2
⇒ y = 1
⇒ (0, 1) = (0, 1)
∴ (0, 1) is the point on h⁻¹(x).
Option (D): (–5, 1)
put x = -5 in the equation y = (2 - x)/2
⇒ y = 3.5
⇒ (-5, 3.5) ≠ (–5, 1)
∴ (–5, 1) is not the point on h⁻¹(x).
Therefore, the point on the graph of the inverse function of h⁻¹(x) is (0, 1).
Learn about the Inverse Function here: https://brainly.com/question/16406473?referrer=searchResults
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