CBSE (Science) Class 11CBSE
Share

Books Shortlist

If 3 F ( X ) + 5 F ( 1 X ) = 1 X − 3 for All Non-zero X, Then F(X) =(A)1 14 ( 3 X + 5 X − 6 )(B) 1 14 ( − 3 X + 5 X − 6 )(C) 1 14 ( − 3 X + 5 X + 6 )(D) None of These - CBSE (Science) Class 11 - Mathematics

Question

If $3f\left( x \right) + 5f\left( \frac{1}{x} \right) = \frac{1}{x} - 3$  for all non-zero x, then f(x) =

• (a)  $\frac{1}{14}\left( \frac{3}{x} + 5x - 6 \right)$

• (b)  $\frac{1}{14}\left( - \frac{3}{x} + 5x - 6 \right)$

• (c) $\frac{1}{14}\left( - \frac{3}{x} + 5x + 6 \right)$

• (d) None of these

Solution

(d) None of these

$3f\left( x \right) + 5f\left( \frac{1}{x} \right) = \frac{1}{x} - 3$

$\text{ Multiplying (1) by } 3:$

$15 f\left( \frac{1}{x} \right) + 9 f(x) = \frac{3}{x} - 9 . . . . . (2)$

$\text{ Replacing x by} \frac{1}{x}\text{ in } (1):$

$3 f\left( \frac{1}{x} \right) + 5 f(x) = x - 3$

$\text{ Multiplying by } 5:$

$15 f\left( \frac{1}{x} \right) + 25 f(x) = 5x - 15 . . . . (3)$

$\text{ Solving (2) and (3) } :$

$- 16 f(x) = \frac{3}{x} - 5x + 6$

$\Rightarrow f(x) = \frac{1}{16}\left( - \frac{3}{x} + 5x - 6 \right)$

Notes

Disclaimer: The question in the book has some error, so, none of the options are matching with the solution. The solution is created according to the question given in the book.

Is there an error in this question or solution?

APPEARS IN

Solution If 3 F ( X ) + 5 F ( 1 X ) = 1 X − 3 for All Non-zero X, Then F(X) =(A)1 14 ( 3 X + 5 X − 6 )(B) 1 14 ( − 3 X + 5 X − 6 )(C) 1 14 ( − 3 X + 5 X + 6 )(D) None of These Concept: Functions.
S