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What is the inverse of the function # f(x) = x +3 #?

Answer 1

#f^(-1)(x)=x-3#

To find the inverse of a function, just "trade" #x# and #y# and solve for the "new" #y#. The graph of the inverse is the reflection of the original function over the line #y=x#.

Rewrite the function #f(x)=x+3#

as the equation #y=x+3#

Trade #x# and #y#.

#x=y+3#

Solve for the "new" #y#.

#xcolor(white)(aaa)=y+3# #color(white)(a)-3color(white)(a^2aa)-3color(white)(aaa)#Subtract 3 from both sides

#x-3=y#

#y=x-3#

The symbol for the inverse is #f^(-1)(x)#

#f^(-1)(x)=x-3#

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Answer 2

Lincoln Anderson

The inverse of the function ( f(x) = x + 3 ) is ( f^{-1}(x) = x - 3 ).

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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.