1. Are the functions f, g and h given below linearly independent?
f(x) = e^3x + cos(7x), g(x) = e^3x − cos(7x), h(x) = cos(7x).
2. If they are independent, enter all zeroes. If they are not linearly independent, find a nontrivial solution to the equation below. Be sure you can justify your answer.
………...(e^3x−cos(7x)) + ……………….(e^3x+cos(7x)) + …………..(cos(7x))=0.

First step is to get rid of the square root. remember that a square root is the same as raising to the (1/2) power. see below: multiply exponents per exponent rules to get: remember you subtract exponents from the denominator and add exponents in the numerator so: simplify further: so a is the correct choice. if you don't understand this google exponent rules and it will you understand. look at the image results.