Let # f(x)= 4x+3# and #g(x)= 1/(x+2)#, how do you evaluate f(g(x)) and g(f(x)) for x?
Redefine the equations as follows:
You can then evaluate the new functions using these definitions.
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To evaluate ( f(g(x)) ) and ( g(f(x)) ) for ( x ), follow these steps:
 Substitute the function ( g(x) ) into the function ( f(x) ) to evaluate ( f(g(x)) ).
 Substitute the function ( f(x) ) into the function ( g(x) ) to evaluate ( g(f(x)) ).
Let's compute these:

Evaluate ( f(g(x)) ): [ f(g(x)) = f\left(\frac{1}{x+2}\right) = 4\left(\frac{1}{x+2}\right) + 3 = \frac{4}{x+2} + 3 ]

Evaluate ( g(f(x)) ): [ g(f(x)) = g(4x + 3) = \frac{1}{(4x + 3) + 2} = \frac{1}{4x + 5} ]
So, ( f(g(x)) = \frac{4}{x+2} + 3 ) and ( g(f(x)) = \frac{1}{4x + 5} ).
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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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