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inverse function question help

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?
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Avatar for Zacken
Zacken
22
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 f(x)f(x) and f−1(x)f^{-1}(x). You'll see that they intersect only along the line y=xy=x. Hence any solution to f(x)=f−1(x)f(x) = f^{-1}(x) will be equivalent to f(x)=xf(x) = x or f−1(x)=xf^{-1}(x) = x.

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.
(edited 7 years ago)
Reply 2
Avatar for alvan15
alvan15
OP
11
[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 f(x)f(x) and f−1(x)f^{-1}(x). You'll see that they intersect only along the line y=xy=x. Hence any solution to f(x)=f−1(x)f(x) = f^{-1}(x) will be equivalent to f(x)=xf(x) = x or f−1(x)=xf^{-1}(x) = x.

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 :smile:
Reply 3
Avatar for Zacken
Zacken
22
Original post by alvan15

thank you so much , i totally get it now , appreciate the help, have a nice day :smile:


No problem

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