Given functions $f (x) = ln (x - 1)$ for $x > 1$ and $g (x) = e^{2 x} + 1$ for $x \in R$ , find the rule and range of the composite function $f g (x)$ .

Practise more Functions, Graphing Techniques and Transformations.

Free questions with an explanation for every one, and full timed Singapore GCE A-Level mock tests.

All Functions, Graphing Techniques and Transformations questions Take a mock test

More Functions, Graphing Techniques and Transformations questions

The function $f$ is defined by $f : x \mapsto \frac{2 x + 1}{x - 3}$ for $x \in R, x > 3$ . Find the rule and domain of the inverse fu…
The curve $C$ with equation $y = f (x)$ undergoes a transformation: first a stretch by factor $2$ parallel to the $x$ -axis, followed by a tra…
Find all asymptotes of the rational curve $y = \frac{2 x ^{2} - 5 x + 1}{x - 2}$ .
Let $f (x) = x^{2} - 4 x + 7$ for $x \in R$ . What is the least value of $k$ such that the restricted function $g (x) = f (x)$ for…
The curve $y = \frac{a x + b}{c x + d}$ has asymptotes $x = 3$ and $y = 2$ , and passes through the point $(1, 0)$ . Find the value of…
Find $f^{- 1} (x)$ for $f (x) = \frac{3 x - 2}{x + 1}$ , $x \neq = - 1$ .

Given functions f(x) = ln (x - 1)… | Singapore GCE A-Level