The functions $f$ and $g$ are given by $f(x) = x^2 - 4x + 3$ for $x > c$, where $c$ is a constant, and $g(x) = \frac{1}{x+1}$ for $x > -1$.
(a)[2]
Express $f(x)$ so that it is written as $(x-a)^2 + b$.
(b)[1]
State the minimum value of $c$.
(c)[3]
Find an expression for $f^{-1}(x)$ and state the domain for $f^{-1}$.
(d)[3]
Find an expression for $gf(x)$ and state the range of values of $gf$.
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This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Complete the square to obtain $(x-2)^2-1$” …
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