1. Decide whether the solutions to each equation are rational or irrational. Explain your reasoning.
a. \( ( x + 5 ) ^ { 2 } = 9 \)
b. \( ( x + 5 ) ^ { 2 } = 10 \)
2. Someone says that if you add two irrational numbers, you will always get an irrational sum. How can you convince the person they are wrong?
a) rational
b) irrational
Find the inverse for each of the following functions.
\(f ( x ) = 3 x + 1\)
\(g ( x ) = 1 x ^ { 3 } - 5\)
\(h ( x ) = \frac { 3 } { x + 5 }\)
\(j ( x ) = \sqrt[ 3 ] { x + 1 }\)
The total revenue from the sale of a popular book is approximated by the rational function \( R ( x ) = \frac { 1700 x ^ { 2 } } { x ^ { 2 } + 4 } \) , where \( x \) is the number of years since publication and \( R ( x ) \)
is the total revenue in millions of dollars.
(a) Find the total revenue at the end of the first year.
(b) Find the total revenue at the end of the second year.
