यदि f(x) + 2f() =  है, तो f(x) का मान क्या है?

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Option 4 :
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गणना:

यहाँ, f(x) + 2f() =                 ....(1)

x को  से प्रतिस्थापित करने पर, हमें निम्न प्राप्त होता है

f() + 2f(x) = x                          ....(2)

(1) और (2) को जोड़ने पर, हमें निम्न प्राप्त होता है

 3f(x) + 3f()) = x +                ....(3)

अब, (1) को (2) में से घटाने पर, हमें निम्न प्राप्त होता है

f(x) - f() = x - 

3 से गुणा करने पर,

3f(x) - 3f() = 3x -                   ....(4)

अब, (3) और (4) को जोड़ने पर, हमें निम्न प्राप्त होता है

6f(x) = 4x - 

f(x) = 

अतः, विकल्प (4) सही है।     

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