(ii) State the smallest possible value of $m$ for which $f$ is one-one.

The function $\mathrm{f}:x\mapsto x^2-4x+k$ is defined for the domain $x⩾p$, where $k \& p$ are constants.

(i) Express $f\left(x\right)$ in the form $(x+a{)}^2+b+k$, where $a \& b$ are constants.

The function $\mathrm{f}:x\mapsto x^2-4x+k$ is defined for the domain $x⩾p$, where $k \& p$ are constants.

(ii) State the range of $\mathrm{f}$ in terms of $k$.

The function $\mathrm{f}:x\mapsto x^2-4x+k$ is defined for the domain $x⩾p$, where $k \& p$ are constants.

(iii) State the smallest value of $p$ for which $\mathrm{f}$ is one-one.

The function $\mathrm{f}:x\mapsto x^2-4x+k$ is defined for the domain $x⩾p$, where $k \& p$ are constants.

(iv) For the value of $p$ found in part iii, find an expression for $f^{-1}\left(x\right)$ and state the domain of $f$ ? giving your answer in terms of $k$.

The diagram shows the function $f$ defined for $-1⩽x⩽4$, where
$f\left(x\right)=\left\{\begin{array}{l}\begin{array}{cc}3x-2& \text{for} -1⩽x⩽1\end{array}\\ \begin{array}{cc}\frac{4}{5-x}& \text{for} 1<x⩽4\end{array}\end{array}\right.$.

(i) State the range of $f$.

The diagram shows the function $f$ defined for $-1⩽x⩽4$, where
$f\left(x\right)=\left\{\begin{array}{l}\begin{array}{cc}3x-2& \text{for} -1⩽x⩽1\end{array}\\ \begin{array}{cc}\frac{4}{5-x}& \text{for} 1<x⩽4\end{array}\end{array}\right.$.
Copy the diagram and on your copy sketch the graph of $y=f^{-1}\left(x\right)$.

The diagram shows the function $f$ defined for $-1⩽x⩽4$, where
$f\left(x\right)=\left\{\begin{array}{l}\begin{array}{cc}3x-2& \text{for} -1⩽x⩽1\end{array}\\ \begin{array}{cc}\frac{4}{5-x}& \text{for} 1<x⩽4\end{array}\end{array}\right.$.
(iii) Obtain expressions to define the function $f^{-1}$, giving also the set of values for which each expression is valid.