Let f, g : R → R+ defined by f (x) = 2x + 3 and g(x) = x2. Find (f ◦ g)(x) and (g ◦ f )(x)
Question
Let f, g : R → R+ defined by f (x) = 2x + 3 and g(x) = x2. Find (f ◦ g)(x) and (g ◦ f )(x)
Solution
To find the composition of two functions, you substitute the output of one function into the other function.
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For (f ◦ g)(x), you substitute g(x) into f(x).
So, f(g(x)) = f(x^2) = 2x^2 + 3.
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For (g ◦ f)(x), you substitute f(x) into g(x).
So, g(f(x)) = g(2x + 3) = (2x + 3)^2.
So, (f ◦ g)(x) = 2x^2 + 3 and (g ◦ f )(x) = (2x + 3)^2.
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