# How do you find the compositions given # f(x)=8x-1# and #g(x)=x/2#?

To find the composition of two functions, denoted as ( f(g(x)) ) or ( g(f(x)) ), you substitute the expression for one function into the other function.

For ( f(g(x)) ): [ f(g(x)) = f\left(\frac{x}{2}\right) ] [ = 8\left(\frac{x}{2}\right) - 1 ] [ = 4x - 1 ]

For ( g(f(x)) ): [ g(f(x)) = g(8x - 1) ] [ = \frac{8x - 1}{2} ] [ = 4x - \frac{1}{2} ]

So, the compositions are: [ f(g(x)) = 4x - 1 ] [ g(f(x)) = 4x - \frac{1}{2} ]

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Substitute the expression for

Similarly find:

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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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