- The function f is defined by
$$f ( x ) = \frac { 2 x ^ { 2 } - 32 } { 3 x ^ { 2 } + 7 x - 20 } + \frac { 8 } { 3 x - 5 } \quad x \in \mathbb { R } \quad x > 2$$
- Show that \(\mathrm { f } ( x ) = \frac { 2 x } { 3 x - 5 }\)
- Show, using calculus, that f is a decreasing function.
You must make your reasoning clear.
The function g is defined by
$$g ( x ) = 3 + 2 \ln x \quad x \geqslant 1$$
- Find \(\mathrm { g } ^ { - 1 }\)
- Find the exact value of \(a\) for which
$$\operatorname { gf } ( a ) = 5$$