To find an inverse function from a given function, here’s what you need to do:
Know that inverses "undo" each other: If you have a function called ( f(x) ), its inverse is written as ( f^{-1}(x) ). They work together like this: when you plug the output of one into the other, you get back to where you started. In math terms, we write this as ( f(f^{-1}(x)) = x ).
Switch ( x ) and ( y ): If your function is written as ( y = f(x) ), change it so that ( f(x) ) becomes ( y ). Then, switch ( x ) and ( y ) around. This means wherever you see ( x ), put ( y ), and wherever you see ( y ), put ( x ).
Solve for ( y ): Now, you need to rearrange the equation to express ( y ) in terms of ( x ). After doing this, you’ll have your inverse function!
Double-check your work: To make sure you did it right, try plugging some numbers into both functions. If they really are inverses, you should get back to your starting number.
Following these steps has really helped me understand inverse functions better in Algebra!
To find an inverse function from a given function, here’s what you need to do:
Know that inverses "undo" each other: If you have a function called ( f(x) ), its inverse is written as ( f^{-1}(x) ). They work together like this: when you plug the output of one into the other, you get back to where you started. In math terms, we write this as ( f(f^{-1}(x)) = x ).
Switch ( x ) and ( y ): If your function is written as ( y = f(x) ), change it so that ( f(x) ) becomes ( y ). Then, switch ( x ) and ( y ) around. This means wherever you see ( x ), put ( y ), and wherever you see ( y ), put ( x ).
Solve for ( y ): Now, you need to rearrange the equation to express ( y ) in terms of ( x ). After doing this, you’ll have your inverse function!
Double-check your work: To make sure you did it right, try plugging some numbers into both functions. If they really are inverses, you should get back to your starting number.
Following these steps has really helped me understand inverse functions better in Algebra!