# Exam-Style Question on Inverse Functions

## A mathematics exam-style question with a worked solution that can be revealed gradually

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Question id: 356. This question is similar to one that appeared on an IB Standard paper in 2012. The use of a calculator is not allowed.

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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