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 $f:x\mapsto 2x+5$  .
Find the function g if $fg:x\mapsto 3x-8$  .

[Note : First function f is given]

Example 2
A function f is defined by $f:x\mapsto \frac{2}{x}$ .
Find the function g if $fg:x\mapsto x^2+1$   .

[Note : the first function f is given]

Example 3
A function f is defined by $f:x\mapsto 2x+1$  .
Find the function g if $fg:x\mapsto \frac{5x-2}{x+5},x\ne -5$  .

[Note : First function is given]