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

Find the inverse of f(x) = (2x + 5)/(x - 3). Give the domain and the range of f.

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

Find the inverse of $f(x) = \dfrac{2x + 5}{x - 3}$ . Give the domain and the range of $f$ .

Need a reminder? The key ideaShow

$f$ has an inverse exactly when it is one-one and onto. To find $f^{-1}$ , solve $y = f(x)$ for $x$ . Its graph is the reflection of $f$ in $y = x$ , and $(g \circ f)^{-1} = f^{-1} \circ g^{-1}$ .

The worked solution

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Find the inverse of f(x) = (2x + 5)/(x - 3). Give the domain and the range of f.

The worked solution

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