$1\mathrm{.}2$: Operations on Functions

Section $1\mathrm{.}2\mathrm{.}1$: Composite Functions

Definitions

When the output of one function is used as the input of another function, we call the entire operation a composition of functions.

Composite functions can be written as f$$g$=$f$$gx$=$f$($gx$)$ given two functions f and g$.$

f$$gx is read $$f composed with g at x$$ or just $$f of g of x$.$

Examples

Given the equations of the functions, determine the value of each composite function.

f$($x$)=2$x $1$

g$($x$)=$ x$35$

h$($x$)=5$ x$2$

f$$g$3$

h$$g$-1$

f$$g

g$$f