If point (a, b) lies on the graph y=f(x), the graph of f^-1 (x) must contain point:

By the definition of inverse function,the point (a,b) lies on the graph So, (b,a) must be lies on the graph of .

Given:

Point (a,b) lies on the graph y= f(x).

Find:

The graph of   must contain that point.

As per the definition of inverse function, if two one-to-one functions f(x) and g(x). If (f∘g)(x)=x and (g∘f)(x)=x. Then, we say that f(x) and g(x) are inverses of each other.

Then, its inverse is defined as

Therefore, we have to interchange x and y-coordinate of the points which lies on the function f to get f⁻¹.

Thus, the point (a,b) lies on the graph So, (b,a) must be lies on the graph of .

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Given:

Point (a,b) lies on the graph .

To find:

The point which is must be lies on the graph of .

Solution:

According to the definition of an inverse function, if a function is defined as

then, its inverse is defined as

It means, we have to interchange x and y-coordinate of the points which lies on the function f to get f⁻¹.

We have a point (a,b) lies on the graph . So, (b,a) must be lies on the graph of .

Therefore, the correct option is (1).

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