HardMathematicsHigh School (11–12)Functions and Calculus › Composite and Inverse FunctionsNumerical

Let f(x) = 1/(x + 2) and g(x) = √x. Find (g ° f)(x) and (f ° g)(x), with their domains.

Try it on paper first. A hint, the key idea and the worked solution are here when you need them.

Let $f(x) = \dfrac{1}{x + 2}$ and $g(x) = \sqrt{x}$ . Find $(g \circ f)(x)$ and $(f \circ g)(x)$ , with their domains.

Need a reminder? The key ideaShow

$(g \circ f)(x) = g(f(x))$ : do $f$ first. The domain of $g \circ f$ holds the $x$ in the domain of $f$ whose $f(x)$ is in the domain of $g$ . Usually $g \circ f \neq f \circ g$ .

The worked solution

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Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.

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Let f(x) = 1/(x + 2) and g(x) = √x. Find (g ° f)(x) and (f ° g)(x), with their domains.

The worked solution

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