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# inverse function question help watch

1. why is that when i want to solve for value of x so a function equals its inverse function

f(x) = f-1(x) (the -1 is suppose to be small)

how come the inverse function can be substituted with x?

for example , f(x) = x^2 - 3

√x+3 = x^2 - 3 can be worked out with x^2 - 3 = x

why is f(x) = f-1(x) equals to f(x) = x ?

could that be because the x and y are reversed in inverse function so by inputting x value i'm actually imputing its y value and outputting the x value?
2. (Original post by alvan15)
why is that when i want to solve for value of x so a function equals its inverse function
Look at the graph of and . You'll see that they intersect only along the line . Hence any solution to will be equivalent to or .

This phenomenon occurs precisely due to the definition of what it means for a function to be an inverse to another. Specifically, their composition is the identity.
3. [QUOTE=Zacken;69983322]
(Original post by alvan15)
why is that when i want to solve for value of x so a function equals its inverse function
/QUOTE]

Look at the graph of and . You'll see that they intersect only along the line . Hence any solution to will be equivalent to or .

This phenomenon occurs precisely due to the definition of what it means for a function to be an inverse to another. Specifically, their composition is the identity.
thank you so much , i totally get it now , appreciate the help, have a nice day
4. (Original post by alvan15)
thank you so much , i totally get it now , appreciate the help, have a nice day
No problem

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