# If #f(x)=3x# and #g(x)=4x-3#, how do you find f[g(5)] and g[f(5)]?

To find ( f[g(5)] ), we first evaluate ( g(5) ), then substitute the result into ( f(x) ).

[ g(5) = 4(5) - 3 = 20 - 3 = 17 ]

Now, we evaluate ( f(17) ):

[ f(17) = 3(17) = 51 ]

So, ( f[g(5)] = 51 ).

To find ( g[f(5)] ), we first evaluate ( f(5) ), then substitute the result into ( g(x) ).

[ f(5) = 3(5) = 15 ]

Now, we evaluate ( g(15) ):

[ g(15) = 4(15) - 3 = 60 - 3 = 57 ]

So, ( g[f(5)] = 57 ).

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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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