Express your answer as a polynomial in standard form.f, of, x, equals, 5, x, minus, 4f(x)=5x−4g, of, x, equals, x, squared, minus, 3, x, minus, 11g(x)=x 2 −3x−11Find: , left parenthesis, f, circle, g, right parenthesis, left parenthesis, x, right parenthesisFind: (f∘g)(x)
Question
Express your answer as a polynomial in standard form.f, of, x, equals, 5, x, minus, 4f(x)=5x−4g, of, x, equals, x, squared, minus, 3, x, minus, 11g(x)=x 2 −3x−11Find: , left parenthesis, f, circle, g, right parenthesis, left parenthesis, x, right parenthesisFind: (f∘g)(x)
Solution
To find (f∘g)(x), we need to substitute g(x) into f(x).
Given: f(x) = 5x - 4 g(x) = x^2 - 3x - 11
Substitute g(x) into f(x):
(f∘g)(x) = f(g(x)) = 5(g(x)) - 4 = 5(x^2 - 3x - 11) - 4
Now, distribute the 5:
= 5x^2 - 15x - 55 - 4
Combine like terms:
= 5x^2 - 15x - 59
So, (f∘g)(x) = 5x^2 - 15x - 59. This is the polynomial in standard form.
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