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How do you find #f^-1(x)# given #f(x)=-x-2#?

Answer 1

Benjamin Achtenberg

THe answer is #f^(-1)(x)=-x-2#

Let #y=-x-2#

Then, #x=-y-2#

so, #f^(-1)(x)=-x-2#

Verification,

#f(f^(-1)(x))=f(-x-2)=-(-x-2)-2#

#=x+2-2=x#

Therefore, this confirm that #f^(-1)(x)=-x-2#

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Answer 2

Cora Alexander

To find the inverse of a function ( f(x) ), denoted as ( f^{-1}(x) ), when given the function ( f(x) = -x - 2 ), follow these steps:

Replace ( f(x) ) with ( y ): ( y = -x - 2 )
Swap the variables ( x ) and ( y ): ( x = -y - 2 )
Solve for ( y ) in terms of ( x ): [ x = -y - 2 ] [ x + 2 = -y ] [ y = -x - 2 ]
Replace ( y ) with ( f^{-1}(x) ): ( f^{-1}(x) = -x - 2 )

Therefore, the inverse function ( f^{-1}(x) ) for the given function ( f(x) = -x - 2 ) is ( f^{-1}(x) = -x - 2 ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.