For the given functions, find \((f\circ g)(x)\) and \((g\circ f)(x)\) and the domain of each. \(f(x) = 5x + 1, g(x) = \sqrt{x}\) \((f\circ g)(x) = \) \((g\circ f)(x) = \) The domain of \(f\circ g\) is \( \) (Type your answer in interval notation.) The domain of \(g\circ f\) is \( \) (Type your answer in interval notation. Use integers or fractions for any numbers in the expression.)
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First, let's find f o g(x): (f o g)(x) = f(g(x)) Substituting g(x) into f(x), we get: (f o g)(x) = f(x) = 5 + 1 So, (f o g)(x) = 5 + 1 The domain of f o g is the same as the domain of g(x), which is all real numbers. Show more…
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