# What is the inverse function of #h(x)= 3-(x+4)/(x-7)#?

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To find the inverse function of ( h(x) = 3 - \frac{x+4}{x-7} ), you first need to switch the roles of ( x ) and ( y ), then solve for ( y ).

[ x = 3 - \frac{y+4}{y-7} ]

Then, solve for ( y ) in terms of ( x ).

[ x(y - 7) = 3(y + 4) - (y + 4) ]

[ xy - 7x = 3y + 12 - y - 4 ]

[ xy - 7x = 2y + 8 ]

[ xy - 2y = 7x + 8 ]

[ y(x - 2) = 7x + 8 ]

[ y = \frac{7x + 8}{x - 2} ]

So, the inverse function of ( h(x) ) is ( h^{-1}(x) = \frac{7x + 8}{x - 2} ).

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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.

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.

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.

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