Question

Is the inverse of f(x)=x^2 is also a function true or false

Answer 1

Solution:

The given statement is False.

Explanation:

We have been given the equation $f(x)=x^2$

In order to check whether the inverse is a function or not, we can perform horizontal line test.

Horizontal line test:- If a horizontal line intersects the graph at more than one point then the inverse is not a function. If it intersects at exactly one point then the inverse is a function.

The given equation represents a upward parabola shown in the attached image. The vertex of the parabola is at origin.

Now, we draw a horizontal line and check the number of intersection point of the line and the parabola. We can see that the horizontal line intersects the parabola at two points.

Hence, from horizontal line test, the inverse is a not a function.

Therefore, the given statement is False.