How do you find the inverse of #f(x)= x+1+4# and is it a function?
For the inverse, solve for x, from there equations.
to be combined as
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To find the inverse of the function ( f(x) = x+1 + 4 ), we follow these steps:
 Replace ( f(x) ) with ( y ).
 Swap the roles of ( x ) and ( y ).
 Solve the resulting equation for ( y ).
 Replace ( y ) with ( f^{1}(x) ) to express the inverse function.
So, let's follow these steps:

Replace ( f(x) ) with ( y ): [ y = x+1 + 4 ]

Swap the roles of ( x ) and ( y ): [ x = y+1 + 4 ]

Solve for ( y ): [ x  4 = y + 1 ]
When ( x \geq 4 ): [ (x  4) = y + 1 ] [ y + 1 = 4  x ]
When ( x < 4 ): [ x  4 = y + 1 ] [ y + 1 = x  4 ]
Solve each equation separately for ( y ).

Replace ( y ) with ( f^{1}(x) ) to express the inverse function.
Considering the two cases separately, the inverse function would be:
[ f^{1}(x) = \begin{cases} 4  x & \text{if } x \geq 4 \ x  4 & \text{if } x < 4 \end{cases} ]
This function is indeed a function because each input ( x ) corresponds to exactly one output ( y ). Therefore, it passes the vertical line test.
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When evaluating a onesided 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.
When evaluating a onesided 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.
When evaluating a onesided 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.
When evaluating a onesided 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.
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