# Given #f(x) = (3-2x) / (2x+1)# and #f(g(x)) = 7 - 3x# how do you find g(x)?

To find ( g(x) ), we need to express ( f(g(x)) ) in terms of ( g(x) ) and then compare it with the given expression ( f(g(x)) = 7 - 3x ).

Given ( f(x) = \frac{{3 - 2x}}{{2x + 1}} ) and ( f(g(x)) = 7 - 3x ), we can express ( f(g(x)) ) as:

[ f(g(x)) = \frac{{3 - 2g(x)}}{{2g(x) + 1}} = 7 - 3x ]

By comparing the numerators and denominators, we can write:

[ 3 - 2g(x) = 7 - 3x ] [ 2g(x) + 1 = -3x ]

Now, solve this system of equations for ( g(x) ):

From the second equation, we have:

[ 2g(x) = -3x - 1 ] [ g(x) = \frac{{-3x - 1}}{2} ]

So, ( g(x) = -\frac{{3x}}{2} - \frac{1}{2} ).

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Thus, we have

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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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