Category Archives: 3.5 Combination of Functions; Composition of Functions

Example:

Evaluate (g/f)(-3) when g(x)=x^2-5 and f(x)=sqrt{x+3}

Solution:

Evaluate the function
Rewrite the expression
Replace x with -3 in each function	$(g/f)(-3)={(-3)^2-5}/{sqrt{-3+3}}$
Simplify	$(g/f)(-3)={(-3)^2-5}/{sqrt{-3+3}}$
Division by zero is undefined	is undefined

(g/f)(-3) is undefined.

Composition of Functions

Example:

Find (f circ g)(x) when

f(x)=8x-9 and g(x)={7}/{x+9}

Solution:

The definition of composition
Replace each x in f with g(x)
Simplify and write a single fraction by finding a common denominator
Simplify by using the distributive property and combine like terms.