# How do you find the inverse of #f(x) = x – 7# and is it a function?

The inverse function is

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To find the inverse of a function ( f(x) ), you swap the roles of ( x ) and ( y ), then solve for ( y ).

Given ( f(x) = x - 7 ), let ( y = f(x) ), then ( x = y - 7 ).

To find the inverse, solve for ( y ): [ x = y - 7 ] [ x + 7 = y ]

So, the inverse function ( f^{-1}(x) ) is ( f^{-1}(x) = x + 7 ).

To determine if it is a function, we need to check if each input in the original function corresponds to exactly one output, and vice versa.

Since every value of ( x ) corresponds to exactly one value of ( y ) in both ( f(x) ) and ( f^{-1}(x) ), and every value of ( y ) corresponds to exactly one value of ( x ) in both functions, then both ( f(x) ) and ( f^{-1}(x) ) are functions.

Therefore, ( f^{-1}(x) = x + 7 ) is a function.

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