How do you find the compositions given #g(x) = 3x + 2# and #h(x) = 9x^2 + 12x + 9#?
Function compositions are basically plugging one function into another function.
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To find the compositions, you would substitute the expression for one function into the other function. For ( g(x) = 3x + 2 ) and ( h(x) = 9x^2 + 12x + 9 ), the compositions would be ( g(h(x)) ) and ( h(g(x)) ).

To find ( g(h(x)) ), substitute ( h(x) ) into ( g(x) ), so you would replace ( x ) in ( g(x) ) with ( h(x) ). [ g(h(x)) = 3(9x^2 + 12x + 9) + 2 ] Simplify this expression to find ( g(h(x)) ).

To find ( h(g(x)) ), substitute ( g(x) ) into ( h(x) ), so you would replace ( x ) in ( h(x) ) with ( g(x) ). [ h(g(x)) = 9(3x + 2)^2 + 12(3x + 2) + 9 ] Simplify this expression to find ( h(g(x)) ).
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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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