The functions $f\,$ and $g\,$ are defined by

$\mapsto \ln(3x - 2)$ , $\in \mathbb{R}$ , $x>23\displaystyle x > \frac{2}{3}$

$g:x↦3x−2\displaystyle g : x \mapsto \frac{3}{x - 2}$ , $\in \mathbb{R}$ , $\neq 2$

Find the exact value of $f g (3)$ .

Find an expression for $f^{-1}(x)$ and, using set notation, state its domain.

Find the exact values of $x\,$ for which $∣ g (x) ∣ = 4$ .

The functions $f\,$ and $g\,$ are defined by

$\mapsto \ln(3x - 2)$ , $\in \mathbb{R}$ , $x>23\displaystyle x > \frac{2}{3}$

$g:x↦3x−2\displaystyle g : x \mapsto \frac{3}{x - 2}$ , $\in \mathbb{R}$ , $\neq 2$

Find the exact value of $f g (3)$ .

Find an expression for $f^{-1}(x)$ and, using set notation, state its domain.

Find the exact values of $x\,$ for which $∣ g (x) ∣ = 4$ .

1 Pure Mathematics

1 Pure Mathematics Questions