IB DP Math MAA SL : IB Style Mock Exams – Set 4 Paper 1

(a)
From the graph, at \(x = -3\), the value of \(y\) is \(-1\).
\(f(-3) = -1\)

(b)
The domain of the inverse function \(f^{-1}\) is equivalent to the range of the original function \(f\).
The \(y\)-values on the graph range from \(-3\) to \(5\).
Domain: \([-3, 5]\)

(c)
If \(f^{-1}(2x – 7) = -3\), then by definition \(f(-3) = 2x – 7\).
Using the result from (a) where \(f(-3) = -1\):
\(-1 = 2x – 7\)
\(6 = 2x\)
\(x = 3\)