How do you find the inverse of #f(x)= x+1+4#?
The function
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To find the inverse of ( f(x) = x+1 + 4 ):

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

Swap ( x ) and ( y ): ( x = y+1 + 4 ).

Solve for ( y ):
 Subtract 4 from both sides: ( x  4 = y+1 ).
 Multiply both sides by 1: ( 4  x = y+1 ).

Solve for ( y+1 ):
 If ( 4  x \geq 0 ), then ( 4  x = y + 1 ).
 Subtract 1 from both sides: ( 3  x = y ).
 If ( 4  x < 0 ), then ( 4  x = (y + 1) ).
 Multiply both sides by 1: ( x  4 = y + 1 ).
 Subtract 1 from both sides: ( x  5 = y ).
 If ( 4  x \geq 0 ), then ( 4  x = y + 1 ).

Combine both cases:
 ( y = \begin{cases} 3  x & \text{if } x \leq 4 \ x  5 & \text{if } x > 4 \end{cases} ).
Therefore, the inverse function is ( f^{1}(x) = \begin{cases} 3  x & \text{if } x \leq 4 \ x  5 & \text{if } x > 4 \end{cases} ).
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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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