# How do you find the inverse of #f(x)=x^2-6x#?

Now swap back the x for the variable y.

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To find the inverse of ( f(x) = x^2 - 6x ), follow these steps:

- Replace ( f(x) ) with ( y ).
- Swap ( x ) and ( y ) to get ( x = y^2 - 6y ).
- Rearrange the equation to solve for ( y ): ( y^2 - 6y - x = 0 ).
- Use the quadratic formula: ( y = \frac{{6 \pm \sqrt{{6^2 - 4(1)(-x)}}}}{{2(1)}} ).
- Simplify the expression: ( y = \frac{{6 \pm \sqrt{{36 + 4x}}}}{{2}} ).
- This gives you two possible values for ( y ), so the inverse functions are: ( f^{-1}(x) = 3 + \sqrt{{x + 9}} ) and ( f^{-1}(x) = 3 - \sqrt{{x + 9}} ).

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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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- How do you find the asymptotes for #f(x) =(x^2)/(x-1)#?
- What transformation can you apply to #y=sqrtx# to obtain the graph #y=-2sqrt(3(x-4))+9#?
- How do you identify all asymptotes or holes for #f(x)=(x^2-x)/(2x^2+4x-6)#?
- What are some examples of functions with asymptotes?

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