Respuesta :

Given:

Point (a,b) lies on the graph [tex]y=f(x)[/tex].

To find:

The point which is must be lies on the graph of [tex]y=f^{-1}(x)[/tex].

Solution:

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

[tex]f=\{(x,y):x\in R,y\in R\}[/tex]

then, its inverse is defined as

[tex]f^{-1}=\{(y,x):x\in R,y\in R\}[/tex]

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 [tex]y=f(x)[/tex]. So, (b,a) must be lies on the graph of [tex]y=f^{-1}(x)[/tex].

Therefore, the correct option is (1).

shristiparmar1221

By the definition of inverse function,the point (a,b) lies on the graph [tex]\bold{y= f(x).}[/tex] So, (b,a) must be lies on the graph of [tex]\bold{y=f^{-1} (x)}[/tex].

Given:

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

Find:

The graph of  [tex]\bold{y=f^{-1} (x)}[/tex] 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.

[tex]\bold{f=\{ (x,y):x\epsilon R,y\epsilon R\}}[/tex]

Then, its inverse is defined as

[tex]\bold{f^{-1} =\{ (y,x):x\epsilon R,y\epsilon R\}}[/tex]

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 [tex]y= f(x).[/tex] So, (b,a) must be lies on the graph of [tex]y=f^{-1} (x)[/tex].

For more details, prefer this link :

https://brainly.com/question/10300045

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