Question

A certain function f satisfies the equation f(x)+2*f(6-x) = x for all real numbers x. the value of f(1) is

a.2

b.can't determine

c.1

d.3

Answer 1

Answer :

Given that,

f (x) + 2 * f (6 - x) = x

When x = 1,

f (1) + 2 * f (5) = 1 ...(i)

When x = 5,

f (5) + 2 * f (1) = 5

⇒ 2 * {f (5) + 2 * f (1)} = 2 * 5

⇒ 2 * f (5) + 4 * f (1) = 10 ...(ii)

Now, (ii) - (i) ⇒

2 * f (5) + 4 * f (1) - f (1) - 2 * f (5) = 10 - 1

⇒ 3 * f (1) = 9

⇒ f (1) = 9/3

⇒ f (1) = 3

Thus, option (c) is correct

#MarkAsBrainliest