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`f: RvecR ,f(x^2=x+3)+2f(x^2-3x+5)=6x^2-10 x+17AAx in R ,`then find the function `f(x)dot` |
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Answer» Correct Answer - `f(x)=2x-3` Obviously, `f` is a linear polynomial. Let `f(x)=ax+b.` Hence, `f(x^(2)+x+3)+2f(x^(2)-3x+5)=6x^(2)-10x+17` or ` [a(x^(2)+x+3)+b]+2[a(x^(2)-3x+5)+b]=6x^(2)-10x+17` or `a+2a=6 " (1) " ` and `a-6a= -10 " (2)" ` or `a=2 " " ` (Comparing coeff. of `x^(2)` and coeff. of `x` both sides) Again, `3a+b+10a+2b=17` or `6+b+20+2b=17` ` :. b= -3` or `f(x)=2x-3` |
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