HardMathematicsHigh School (11–12)Functions and Calculus › Composite and Inverse FunctionsConceptualBoard Exam AP A-Level IB

Let f(x) = 2x + 3 and g(x) = ax + b. For which a and b is g ° f = f ° g? …

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

Let $f(x) = 2x + 3$ and $g(x) = ax + b$ . For which $a$ and $b$ is $g \circ f = f \circ g$ ? Give one example other than $g = f$ .

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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Let f(x) = 2x + 3 and g(x) = ax + b. For which a and b is g ° f = f ° g? …

The worked solution

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