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Question: What is the domain of f g (x)? f(x)=2x2–10x g(x)= – 5x+4
The domain of f(g(x)) is the set of all real numbers that allows g(x) to be in the domain of f(x). Looking at g(x) = -5x + 4, we can see that it's a linear function and the domain for any linear function is all real numbers. However, the output of g(x) must also be in the domain of f(x) to be included in the domain of f(g(x)). In the given function f(x) = 2x^2 – 10x, the domain is also all real numbers because it's a quadratic function and the domain of any quadratic function is all real numbers. Therefore, the domain of f(g(x)) is all real numbers.
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