Mathematics Pure Math 1 9709: FUNCTIONS Topical Past Paper Questions

A function f is defined by $ f(x) = 3 - \frac{4}{2x + 3} $ for $ x > -\frac{3}{2} $. (a) (i) Find $ f'(x) $. (ii) Hence, show that f is an increasing function. (b) (i) Find an expression for $ f^{-1}(x) $. (ii) State the domain and range of $ f^{-1} $

The function f is defined by $$ \mathrm{f}(x)=3+\frac{7}{x-2} $$ for x > 2. (a) It is given that $ f(a)=4 $. Find the value of $a$. [2] (b) Find an expression for $ f^{-1}(x) $ and state the domain of $ f^{-1} $. [4] (c) The function g is defined by $$ \mathrm{g}(x)=\frac{1+4x}{2…

(a) Express $ 3x^{2}-12x+14 $ in the form $ 3(x+a)^{2}+b $, where a and b are constants to be found. The function $ f(x) = 3x^{2} - 12x + 14 $ is defined for $ x \geqslant k $, where $ k $ is a constant. (b) Find the least value of k for which the function $ f^{-1} $ exists. For…