If f and g are two functions for which f' = g and g' = f for all x, then prove that

f^2 - g^2 must be a constant.

3 answers

ff' = fg
gg' = gf

ff' = gg'
2f f' - 2g g' = 0
f^2 - g^2 = c
I don't really get why f^2 - g^2 would be a constant.
take integrals across the equation

2ff' - 2gg' = 0
∫2f df - ∫2g dg = 0
(f^2 + c1) - (g^2 + c2) = 0
f^2 - g^2 = -(c1+c2) = c
Similar Questions
  1. Unicellular cells must carry out ___ of life.(1 point)Responses a few functions a few functions specific functions specific
    1. answers icon 16 answers
  2. Unicellular cells must carry out ___ of life.(1 point)Responses specific functions specific functions a few functions a few
    1. answers icon 7 answers
    1. answers icon 1 answer
  3. Unicellular cells must carry out ___ of life.Responses specific functions specific functions all functions all functions a few
    1. answers icon 1 answer
more similar questions