Chapter 6 Rational Exponents and Radical Functions - 6.3 Perform Function Operations and Composition - 6.3 Exercises - Skill Practice - Page 432: 2

Sometimes

A power function is written in the form: $$f(x)=ax^b.$$ Consider a second power function: $$g(x)=cx^d.$$ The sum of the two functions is: $$h(x)=f(x)+g(x)=ax^b+cx^d.$$ We notice that the function $h$ can be written as a power function only in case $b=d$: $$h(x)=f(x)+g(x)=ax^b+cx^b=(a+c)x^b.$$ Therefore the given statement is SOMETIMES true.