Question

If xf(x)+xf(1/x)=x+1, what is the value of f(2024)?

130

likes

651 views

Answer to a math question If xf(x)+xf(1/x)=x+1, what is the value of f(2024)?

$Expert avatar$

Gene

4.5

108 Answers

Veja como resolver para f(2024): **1. Substitua x por 1/x:** Na equação x*f(x) + x*f(1/x) = x + 1, substitua x por 1/x: * (1/x) * f(1/x) + (1/x) * f(x) = 1/x + 1 **2. Simplificar:** * f(1/x) + f(x) = 1 + x **3. Seja x = 2024:** Substitua x por 2024 na equação original e na equação da etapa 2: * Original: 2024 *f(2024) + 2024 *f(1/2024) = 2025 * Etapa 2: f(1/2024) + f(2024) = 1 + 2024 = 2025 **4. Resolva o sistema de equações:** Agora você tem duas equações com duas incógnitas: * 2024 * f(2024) + 2024 * f(1/2024) = 2025 * f(1/2024) + f(2024) = 2025 Como ambas as equações são iguais a 2025, podemos igualá-las: * 2024 * f(2024) + 2024 * f(1/2024) = f(1/2024) + f(2024) Simplificar: * 2023 * f(2024) = -2023 * f(1/2024) Divida ambos os lados até 2023: *f(2024) = -f(1/2024) **Não podemos determinar o valor exato de f(2024) sem mais informações sobre a função. No entanto, sabemos que f(2024) é o negativo de f(1/2024).**

Frequently asked questions (FAQs)

What is a necessary condition for two triangles to be congruent?

What is the radian measure of an angle that is equal to 180 degrees?

Math question: Is there a nontrivial solution for the equation x^n + y^n = z^n, where n > 2? (

New questions in Mathematics

Solution to the equation y'' - y' - 6y = 0

Exercise 4 - the line (AC) is perpendicular to the line (AB) - the line (EB) is perpendicular to the line (AB) - the lines (AE) and (BC) intersect at D - AC = 2.4 cm; BD = 2.5 cm: DC = 1.5 cm Determine the area of triangle ABE.

Using the integration by parts method, calculate the integral of [x².ln(1/x)]dx: x 4 /4 x³/6 x 4 /8 x³/3 x 4 /6

The equation of the circle that passes through (5,3) and is tangent to the abscissa axis at x=2 is a.(x-2)^2 (y 3)^2 = 9 b.(x-2)^2 (y-3)^2 = 9 c.(x-2)^2 (y-3)^2 = 4 d.(x-2)^2 (y 1)^2 = 4 e.(x-2)^2 (y-1)^2 = 4

Sean must chose a 6- digit PIN number for his online banking account.Each digit can be chosen from 0 to 9. How many different possible PIN numbers can sean chose.

If the midpoint of point A on the x=3 line and point B on the y=-2 line is C(-2,0), what is the sum of the ordinate of point A and the abscissa of point B?

41/39 - 1/38