Let f: R arrow R be a continuous function such that f (3 x )- f ( x )= x. If f (8)=7, then f (14) is equal to :

Question

Let f: R arrow R be a continuous function such that f (3 x )- f ( x )= x. If f (8)=7, then f (14) is equal to : (A) 4 (B) 10 (C) 11 (D) 16

Tardigrade Admin · Accepted Answer

f(x)-f(x / 3)=x / 3 f(x / 3)-f(x / 32)=x / 32 .... on adding f(x)- displaystyle lim n arrow ∞ f((x/3n))=x((1/3)+(1/32) ldots ∞) f(x)-f(0)=(x/2) f(8)=7 ; f(0)=3 f(x)=x / 2+3 f(14)=10

Q. Let $f : R \to R$ be a continuous function such that $f (3 x) - f (x) = x$ . If $f (8) = 7$ , then $f (14)$ is equal to :

4

10

11

16

$f (x) - f (x /3) = x /3$
$f (x /3) - f (x / 3^{2}) = x / 3^{2}$
.... on adding
$f (x) - n \to \infty lim f (\frac{x}{3 ^{n}}) = x (\frac{1}{3} + \frac{1}{3 ^{2}} \dots \infty)$
$f (x) - f (0) = \frac{x}{2}$
$f (8) = 7; f (0) = 3$
$f (x) = x /2 + 3$
$f (14) = 10$

Q. Let f:R→R be a continuous function such that f(3x)−f(x)=x. If f(8)=7, then f(14) is equal to :

4

10

11

16

f(x)−f(x/3)=x/3 f(x/3)−f(x/32)=x/32 .... on adding f(x)−n→∞lim​f(3nx​)=x(31​+321​…∞) f(x)−f(0)=2x​ f(8)=7;f(0)=3 f(x)=x/2+3 f(14)=10

Q. Let $f : R \to R$ be a continuous function such that $f (3 x) - f (x) = x$ . If $f (8) = 7$ , then $f (14)$ is equal to :

$f (x) - f (x /3) = x /3$
$f (x /3) - f (x / 3^{2}) = x / 3^{2}$
.... on adding
$f (x) - n \to \infty lim f (\frac{x}{3 ^{n}}) = x (\frac{1}{3} + \frac{1}{3 ^{2}} \dots \infty)$
$f (x) - f (0) = \frac{x}{2}$
$f (8) = 7; f (0) = 3$
$f (x) = x /2 + 3$
$f (14) = 10$