How do you find (f o g)(x) and its domain, (g o f)(x) and its domain, (f o g)(2) and (g o f)(2) of the following problem #f(x) = 2x + 3#, #g(x) = 3x 1#?
To find (f o g)(x) and its domain:

Substitute g(x) into f(x):
(f o g)(x) = f(g(x)) = f(3x  1) = 2(3x  1) + 3 = 6x  2 + 3 = 6x + 1. 
The domain of (f o g)(x) is the set of all real numbers since there are no restrictions on the domain of the composed function.
To find (g o f)(x) and its domain:

Substitute f(x) into g(x):
(g o f)(x) = g(f(x)) = g(2x + 3) = 3(2x + 3)  1 = 6x + 9  1 = 6x + 8. 
The domain of (g o f)(x) is the set of all real numbers since there are no restrictions on the domain of the composed function.
To find (f o g)(2) and (g o f)(2):
 Substitute x = 2 into the composed functions: (f o g)(2) = f(g(2)) = f(3(2)  1) = f(7) = 2(7) + 3 = 14 + 3 = 11. (g o f)(2) = g(f(2)) = g(2(2) + 3) = g(1) = 3(1)  1 = 3  1 = 4.
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This is an assembly of various functions.
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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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