Additional Mathematics 4037: Functions Topical Past Paper Questions

The diagram shows the graph of $y = f(x)$. On the same diagram sketch the graph of $ y = f^{-1}(x) $. [1] (ii) Describe the relationship between the graph of $ f(x) $ and the graph of $ f^{-1}(x) $. [1] (b) A function g is defined by $ g(x) = e^{\sqrt{x-2}} $ for $ x \geq 2 $. (i…

The function f is defined by $ f(x) = 1 - 4x - x^{2} $ for all real values of x. (a) Write $f(x)$ in the form $a-(x+b)^{2}$, where $a$ and $b$ are constants. (b) Find the range of f. [1] The function g is defined by $ g(x) = 1 - 4x - x^{2} $ for $ x \geq k $, where k is a constan…

The functions f and g are defined as follows, for all real values of x. $$ \mathrm{f}(x)=2\sin x+3\cos x $$ $$ g(x)=e^{3x}-1 $$ (a) Find fg(0). (b) Find $\mathrm{gg}(x)$. (c) Solve the equation $ g^{-1}(x)=\frac{1}{3}\ln5 $.