Question

DUŻO PKT i NAJ.....
Dane są funkcje f(x)=[tex](\frac{1}{9} )^{x}[/tex] i g(x)=[tex](\sqrt{3} )^{x}[/tex] . Oblicz wartość wyrażenia
a).
[tex]\frac{f(-4) - f(-2)}{g(4) - g(2)}[/tex]

b).
[tex]\frac{f(-3)*g(-1)}{f(-1)*g(-3)}[/tex]

Answer 1

Odpowiedź:

a)

f(x) = (1/9)ˣ ; g(x) = (√3)ˣ

f(- 4) = (1/9)⁻⁴ = 9⁴

f(- 2) = (1/9)⁻² = 9²

g(4) = (√3)⁴ = (√3)² * (√3)² = 3 * 3 = 9

g(2) = (√3)² = 3

[f(- 4) - f( - 2)] /[g(4) - g(2)] = (9⁴ - 9²)/(9 - 3) = 9²(9² - 1)/6 = 81(81 - 1)/6 =

= 81 * 80 : 6 = 6480 : 6 = 1080

b)

f(- 3) = (1/9)⁻³ = 9³

f(- 1) = (1/9)⁻¹ = 9

g(- 1) = (√3)⁻¹ = 1/(√3) = √3/3

g(- 3) = (√3)⁻³ = 1/(√3)³ = 1/(3√3) = (√3)/(3 * 3) = √3/9

[f(- 3) * g(- 1)]/[f(- 1) * g(- 3)] = (9³ * √3/3)/(9 * √3/9) = 9³/9 : (√3/3 : √3/9) =

= 9³⁻¹ : ( √3/3 * 9/√3) = 9² : 3 = 81 : 3 = 27