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Exam-Style Questions on Inverse FunctionsProblems on Inverse Functions adapted from questions set in previous Mathematics exams. |
1. | IB Standard |
Part of the graph of \(f(x) = {\log _b}(x + 4)\) for \(x > - 4\) is shown below.
The graph passes through A(4, 3) , has an x-intercept at (-3, 0) and has an asymptote at \(x = - 4\).
(a) Find the value of \(b\).The graph of \(f(x)\) is reflected in the line \(y = x\) to give the graph of \(g(x)\).
(b) Write down the y-intercept of the graph of \(g(x)\).
(c) Sketch the graph of \(g(x)\), noting clearly any asymptotes and the image of A.
(d) Find \(g(x)\) in terms of \(x\).
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