For the pair of functions f(x) = 4x2 + 3x + 5 and g(x) = 3x - 3Find (g ∘ f)(x).
Question
For the pair of functions f(x) = 4x2 + 3x + 5 and g(x) = 3x - 3Find (g ∘ f)(x).
Solution
To find the composition of the functions (g ∘ f)(x), you need to substitute f(x) into g(x).
Here are the steps:
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Write down the function for f(x) and g(x):
f(x) = 4x^2 + 3x + 5 g(x) = 3x - 3
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Substitute f(x) into g(x):
g(f(x)) = 3(4x^2 + 3x + 5) - 3
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Distribute the 3 in the equation:
g(f(x)) = 12x^2 + 9x + 15 - 3
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Simplify the equation:
g(f(x)) = 12x^2 + 9x + 12
So, (g ∘ f)(x) = 12x^2 + 9x + 12.
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