Mathematics: FUNCTIONS - ROOTS Topical Past Paper Questions

Let $ f(x)=4-x^{3} $ and $ g(x)=\ln x $, for x>0. (a) Find $ (f\circ g)(x) $. [2] (b) (i) Solve the equation $ (f\circ g)(x)=x $. (ii) Hence or otherwise, given that $ g(2a)=f^{-1}(2a) $, find the value of a. [5]

[Maximum mark: 7] Let $f(x)=x-8$, $g(x)=x^{4}-3$ and $h(x)=f(g(x))$. (a) Find $h(x)$. [2] Let C be a point on the graph of h. The tangent to the graph of h at C is parallel to the graph of f. (b) Find the x-coordinate of C. [5] ◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼◼…

The function $f$ is defined by $f(x) = \frac{2\ln x + 1}{x - 3}$, $0 f^{-1}(x) $. [4]