Suppose a function can be described by 𝑦=𝑓(𝑥). The graphs of the function and the inverse function intersect when𝑦=
Question
Suppose a function can be described by 𝑦=𝑓(𝑥). The graphs of the function and the inverse function intersect when𝑦=
Solution 1
The graphs of the function and its inverse intersect when y = x. This is because the inverse function is a reflection of the original function across the line y = x. Therefore, they intersect on this line.
Solution 2
The graphs of a function and its inverse intersect when y = x.
Here's why:
-
Let's start with the function y = f(x).
-
The inverse of this function is denoted as x = f^-1(y).
-
When you graph both the function and its inverse on the same set of axes, the points where they intersect are the points where y = x.
-
This is because at these points, the output of the function equals the input, and vice versa for the inverse.
-
Therefore, the graphs of the function and the inverse function intersect when y = x.
Similar Questions
The inverse of the function 𝑓(𝑥)=1−4𝑥5 is the function
Question 9 of 10Given the graph of a function, you can perform the horizontal line test to determine whether the inverse is also a function.A.TrueB.False
Graphs of an inverse function are symmetrical to its original function along the line y=x.
Question 7 of 10Given the function F(x), you can get a picture of the graph of its inverse F -1(x) by flipping the original graph of F(x) over the line _____.
Consider the function 𝑎(𝑥)=-𝑥3+8 and function b modeled by this graph.Which statement describes the relationship between the intercepts of functions a and b? A. The y-intercept of b is less than the y-intercept of a. B. The x-intercept of b is greater than the x-intercept of a. C. The y-intercept of b is equal to the y-intercept of a. D. The x-intercept of b is equal to the x-intercept of a.
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.