Functions [MathB topic 2014-2016]

1	(Edexcel/Math B/2014/jan/paper02/q5) Information about the functions f and g is shown in Figure 1 (a) Find (i) f(x), (ii) gf(w), (iii) fg(x).  h is the function such that $h: x\mapsto \; \frac1{x+2},\;x\neq-2$ (b) Find the inverse function $h^{–1}$. Give your answer in the form $h:x\; \mapsto$ ... (c) Hence, or otherwise, solve $h^{–1}(x) = –x$.	3 2 3
2	(Edexcel/Math B/2014/janR/paper01/q26) \( \begin{array}{l}\mathrm{f}: x \mapsto 5 x-4 \\ \mathrm{~g}: x \mapsto 2-\frac{3}{x+10}\end{array} \) (a) Write down the value of x which must be excluded from any domain of g (b) Find the value of g(–2.5). (c) Find and simplify an expression for fg(x). (d) Solve the equation fg(x) = 3	1 1 2 2
3	(Edexcel/Math B/2014/june/paper02/q10) f and g are two functions such that $f(x)=\frac{2}{x-1};\;\;x\neq1$ $g(x)=x^2-3$ (a) Find the value of \( \operatorname{gf}(3) \) (b) Find \( \mathrm{f}^{-1}(x) \) in terms of \( x \). (c) Show that \( \mathrm{gf}^{-1}(x)=\frac{4+4 x-2 x^{2}}{x^{2}} \) (d) State the value of \( x \) which must be excluded from any domain of \( \mathrm{gf}^{-1} \) (e) Find the values of \( x \) for which \( \mathrm{gf}^{-1}(x)=1 \)	1 2 3 1 5
4	(Edexcel/Math B/2014/juneR/paper02/q6) The two functions, f and g , are defined as  \[ \begin{array}{l} \mathrm{f}: x \mapsto 1-2 x \\ \mathrm{~g}: x \mapsto 2 x^{2}-5 \end{array} \] (a) Find the value of (i) \( \mathrm{f}\left(-\frac{2}{3}\right) \) (ii) \( \mathrm{g}(\sqrt{7}) \) (b) Copy and complete \( \mathrm{f}^{-1}: x \mapsto \ldots \) (c) Show that \( \operatorname{gf}(x)=8 x^{2}-8 x-3 \) (d) Solve the equation \( \mathrm{gf}(x)=45 \)	2 2 2 4
5	(Edexcel/Math B/2015/jan/paper01/q17)> The function f is defined for all the values of $f:x \mapsto x^2-6$ Write down (i) the minimum value of f(x), (ii) the range of f. (b) The function g is given by $g:x\mapsto \frac{x}{2x-3}$ State the value of x that must be excluded from any domain of g	2 1
	Click here for Answer