4MA0 Higher June 2017 Paper 4R Q20

EdexcelHigherOld spec6 marksFunctions

20 The functions f and g are such that

\[\mathrm{f}(x) = \frac{1}{x + 5} \quad \text{and} \quad \mathrm{g}(x) = 2x + 3\]

(a) State which value of \(x\) must be excluded from any domain of f. (1)

(b) Find g(10) (1)

(d) Express the inverse function \(\mathrm{g}^{-1}\) in the form \(\mathrm{g}^{-1}(x) = \ldots\) (2)

Scheme	Marks
−5	B1
	(1)

Scheme	Marks
23	B1
	(1)

Scheme	Marks
(f(−7)) = \(\dfrac{1}{-7 + 5}\) or (f(−7)) = \(-\dfrac{1}{2}\) or \(2\left(\dfrac{1}{-7 + 5}\right) + 3\) or \(2 \times -\dfrac{1}{2} + 3\)	M1
2	A1
	(2)

Mark scheme (d)

Scheme	Marks
\(x - 3 = 2y\) or \(\dfrac{x}{2} = y + \dfrac{3}{2}\) or \(y - 3 = 2x\) or \(\dfrac{y}{2} = x + \dfrac{3}{2}\) or \(\dfrac{y - 3}{2}\) or \(\dfrac{y}{2} - \dfrac{3}{2}\)	M1
\(\dfrac{x - 3}{2}\)	A1
	(2)
	(6 marks)

A1: oe

Eg \(\dfrac{x}{2} - \dfrac{3}{2}\)