Question

Diketahui f(x) = a^{x} + a^{-x} dan g(x) = a^{x} - a^{-x}
Tntukanlah:
a. {f(x)}^{2} - {g(x)^{2}
b. g(2x) - f(x) . g(x)


tolong dijawab secepatnya kakak:)

Answer 1

Verified answer

Jawab

f(x) =  aˣ +1/aˣ
g(x)=  aˣ - 1/aˣ

a.  {f(x)}² - {g(x)}²  = ( f(x)  + g(x) ) (f(x) - g(x))
= (aˣ + 1/aˣ + aˣ -1/aˣ)( aˣ + 1/aˣ - aˣ + 1/aˣ)
= (2 aˣ)(2/aˣ)
= 4 (aˣ/aˣ)
= 4(1)
= 4

b.  g(2x) - f(x).g(x)
= ( a²ˣ - 1/a²ˣ) - {aˣ +1/aˣ)(aˣ- 1/aˣ)
=(a²ˣ - 1/a²ˣ)  - (a²ˣ - 1/a²ˣ)
= a²ˣ - 1/a²ˣ - a²ˣ+ 1/a²ˣ
= (a²ˣ - a²ˣ ) + (-1/a²ˣ + 1/a²ˣ)
= 0