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Find [fog](x) and [gof](x), if they exist. State the domain and range for each.

5.f(x) = -3x
g(x) = x +8

6. f(x) = 2x²-x + 1
g(x) = 4x + 3

User YNR
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Given functions:
f(x) = -3x
g(x) = x + 8
To find fog, we need to substitute g(x) into f(x):

f(g(x)) = f(x + 8) = -3(x + 8) = -3x - 24

The domain of fog(x) is the set of all real numbers since g(x) is defined for all real numbers.

The range of fog(x) is also the set of all real numbers since for any value of x, we can find a corresponding value of f(g(x)).

To find gof, we need to substitute f(x) into g(x):

g(f(x)) = g(-3x) = -3x + 8

The domain of gof(x) is the set of all real numbers since f(x) is defined for all real numbers.

The range of gof(x) is the set of all real numbers since for any value of x, we can find a corresponding value of g(f(x)).

Given functions:
f(x) = 2x²-x + 1
g(x) = 4x + 3
To find fog, we need to substitute g(x) into f(x):

f(g(x)) = f(4x + 3) = 2(4x + 3)² - (4x + 3) + 1 = 32x² + 47x + 20

The domain of fog(x) is the set of all real numbers since g(x) is defined for all real numbers.

The range of fog(x) is the set of all real numbers since for any value of x, we can find a corresponding value of f(g(x)).

To find gof, we need to substitute f(x) into g(x):

g(f(x)) = g(2x² - x + 1) = 4(2x² - x + 1) + 3 = 8x² - x + 7

The domain of gof(x) is the set of all real numbers since f(x) is defined for all real numbers.

The range of gof(x) is the set of all real numbers since for any value of x, we can find a corresponding value of g(f(x)).
User Lizardx
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