The inverse of the function graphed below is not a function as it fails to pass the horizontal test. Hence, B. False is the right option.
What is a function?
A function is a relation between a dependent and an independent variable, say y and x respectively, written as y = f(x). Any such relationship will be called a function if and only if, there is only one value of y corresponding to every x.
We check for a graphed relation to be a function using the vertical test.
When is the inverse of a function also a function?
The inverse of a function, say y = f(x), is given as x = f⁻¹(y), is also a function when f⁻¹(y) passes the vertical test, or simply y = f(x) passes the horizontal test.
What are vertical and horizontal tests?
- Vertical test: In the test, vertical lines are taken parallel to the y-axis, and the number of the intersection of the given graph of the relation to this line is tested. If the intersections on every vertical line ≤ 1, then the given relation passes the test, and it is a function.
- Horizontal test: In the test, horizontal lines are taken parallel to the x-axis, and the number of the intersection of the given graph of the relation to this line is tested. If the intersections on every horizontal line ≤ 1, then the given relation passes the test, and its inverse is a function.
How to solve the given question?
In the question, we are asked to tell whether the inverse of the given function graphed is also a function or not.
To check if the inverse is a function, we perform the horizontal test.
The given graph fails to pass the horizontal test, as for almost every line, the graph intersects two times to the line.
For example, the horizontal line y = 5, the graph intersects at two points.
Thus, the inverse of the function graphed below is not a function as it fails to pass the horizontal test. Hence, B. False is the right option.
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