1.4.2 Finding a new function given a composite function (Case B : Second function is given) Example 1 - 3

Example 1 (substitution Method)
A function f is defined by

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

$g f : x \mapsto x^{2} + 3 x + 5$ .

[Note : Second function is given, use substitution y = x + 2]

Example 2 (Substitution Method)
A function f is defined by

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

$g f : x \mapsto \frac{4}{x + 2}, x \neq - 2$ .

[Note : Second function is given , use substitution y = x – 1]

Example 3 (Substitution Method)
A function f is defined by

$f : x \mapsto \frac{7}{x}$ .
Find the function g if

$g f : x \mapsto \frac{10}{2 x + 3}, x \neq - \frac{3}{2}$ .

[Note : Second function is given, use substitution method]

1.4.2 Finding a new function given a composite function (Case B : Second function is given) Example 1 – 3