How do you find the inverse of #f(x)= (100)/(1+2^x)#?
To find the inverse of the function ( f(x) = \frac{100}{1+2^{x}} ), you can follow these steps:
 Replace ( f(x) ) with ( y ) to rewrite the function as an equation: ( y = \frac{100}{1+2^{x}} ).
 Swap the roles of ( x ) and ( y ) in the equation.
 Solve for ( y ) to find the inverse function ( f^{1}(x) ).
Here are the calculations:

Start with ( y = \frac{100}{1+2^{x}} ).

Swap ( x ) and ( y ): ( x = \frac{100}{1+2^{y}} ).

Solve for ( y ): [ x(1+2^{y}) = 100 ] [ 1+2^{y} = \frac{100}{x} ] [ 2^{y} = \frac{100}{x}  1 ] [ 2^{y} = \frac{100x}{x} ] [ y = \log_2\left(\frac{100x}{x}\right) ] [ y = \log_2\left(\frac{100x}{x}\right) ]
Therefore, the inverse of the function ( f(x) = \frac{100}{1+2^{x}} ) is ( f^{1}(x) = \log_2\left(\frac{100x}{x}\right) ).
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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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