Operations on Functions

Question

Given m(x)=x+3, p(x)=sqrt(x+1)

 

Find (m*p)(x) and write the domain of m*p in interval notation.

Answer 1

This just means to multiply functions m(x) and p(x) together.

 

(x + 3)√(x + 1)

 

To find the domain of the product, we look at the square-root factor.  The number under the square-root must be positive or zero.  So the domain can be found by solving this inequality for x.

 

x + 1 ≥ 0