Operations with Functions:
Domain=[-2,∞)
- Sum (f+g)(x)=f(x)+g(x) / Product (f x g)(x)=f(x) x g(x) / Difference (f-g)(x)=f(x)-g(x) / Quotient (f/g)(x)=f(x)/g(x),g(x) cannot equal 0
- The domain consists of those values of x common to the domains of the f and g. The domain of the quotient function is further restricted by excluding any values that make the denominator,g(x), zero.
- Example: (f+g)(x): (f+g)(x)=f(x)+g(x)
Domain=[-2,∞)
- Plug in the equation where the variables are.
- Solve new equation.
- Describe the domain
- Use ( for infinity and use [ for a certain number.
- Composition of Functions
- Example: f(x)=x^2 +1 and g(x)= x-4, [FoG](x), [GoF](x), and [FoG](2).
Define FoG
Replace G with X-4
Substitute X-4 for x
Simplify by distributing and adding
Define GoF
Replace f(x) with x^2-1
Substitute x^2-1 for x in g(x)
Substitute 2 for x in x^2-8x+17