First slide
Functions (XII)
Question

Let f be a function defined on R satisfying the inequality  3f(x)+2f(x+59x1)=10x+30xR,x1 then f(7) is equal to 

Moderate
Solution

Put x = 7

3f(7) +2 f(11) = 100------(1)

Put x= 11,

3(11) +2f(7) = 140 --------(2) 
Add (1) and (2) 

5f(7) +5f(11) = 240

f(7) +f(11) = 48 

Multiply (3) by 2 and subtract from (1) to obtain f(7)=4

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