10 The function f is defined by \(\mathrm { f } : x \mapsto x ^ { 2 } + 4 x\) for \(x \geqslant c\), where \(c\) is a constant. It is given that f is a one-one function.
- State the range of f in terms of \(c\) and find the smallest possible value of \(c\).
The function g is defined by \(\mathrm { g } : x \mapsto a x + b\) for \(x \geqslant 0\), where \(a\) and \(b\) are positive constants. It is given that, when \(c = 0 , \operatorname { gf } ( 1 ) = 11\) and \(\operatorname { fg } ( 1 ) = 21\).
- Write down two equations in \(a\) and \(b\) and solve them to find the values of \(a\) and \(b\).