1.4.1 Finding a new function given a composite function (Case A : First function is given) Example 1 - 3

Example 1
A function f is defined by

f : x \mapsto 2 x + 5

$f : x \mapsto 2 x + 5$ .
Find the function g if

f g : x \mapsto 3 x - 8

$f g : x \mapsto 3 x - 8$ .

[Note : First function f is given]

Example 2
A function f is defined by

f : x \mapsto \frac{2}{x}

$f : x \mapsto \frac{2}{x}$ .
Find the function g if

f g : x \mapsto x^{2} + 1

$f g : x \mapsto x^{2} + 1$ .

[Note : the first function f is given]

Example 3
A function f is defined by

f : x \mapsto 2 x + 1

$f : x \mapsto 2 x + 1$ .
Find the function g if

f g : x \mapsto \frac{5 x - 2}{x + 5}, x \neq - 5

$f g : x \mapsto \frac{5 x - 2}{x + 5}, x \neq - 5$ .

[Note : First function is given]

1.4.1 Finding a new function given a composite function (Case A : First function is given) Example 1 – 3