Question

The function whose graph is reflection about the line x+y=0 of the inverse function
​

Answer 1

Step-by-step explanation:

REFER THIS IMAGE

HOPE THIS HELPS U

Answer 2

Answer:

The complete question is : The function whose graph is the reflection about the line $x+y=0$ of the inverse function $f^{-1}(x)$ of a function $f(x)$ is  __?

The answer is :  $y=-f(-x)$

Step-by-step explanation:

Let $y=f(x)$

We know that inverse of a function is the reflection about line $y=x$

If we replace $y$ with $x$, and $x$ with $y$, we get :

$x=f(y)$

i.e. $y=f^{-1}(x)$

This is how inverse is found out.

$y=f^{-1}(x)$

We need to find the reflection about $x+y=0$

We can replace $y$ with $-x$, and $x$ with $-y$

We get :

$(-x)=f^{-1}(x)\\\\(-y)=f(-x)\\\\y=-f(-x)$

Hence, the answer is $y=-f(-x)$

Inverse function:

A function that can reverse into another function is known as an inverse function or anti function. In other words, the inverse of a function "f" will take $y$ to $x$ if any function "f" takes $x$ to $y$.