5 \f(x)+4 \f ( \frac{4 x+5}{x-4} )=9(2 x+1), where x \in R and x ≠ 4 What is the value of f(7)?

CAT Exam Model Paper 7 with solutions for free online practice

Question : 4 of 60

Marks: +1, -0

5 \f(x)+4 \f\ ( {4 x+5}/{x-4} )=9(2 x+1),

where

x ∈ R

and x ≠ 4
What is the value of f(7)?

Solution:

5 \f(x)+4 \f\ ( {4 x+5}/{x-4} )=9(2 x+1)

....(i)
Putting x = 7 in (i):
5f(7) + 4f(11) =

9 × (2 × 7 + 1)

⇒ 5f(7) + 4f(11) =135...(ii)
Put x = 11 in (i):
5f(11) + 4f(7) =

9 × (2 × 11 + 1)

5f(11) + 4f(7) = 207...(iii)
Solving (ii) & (iii) we get:

\f(7)=- {153}/{9}=-17

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