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83. A non-zero function f (x) is symmetr...

83. A non-zero function f (x) is symmetrical about the line `y=x` then the value of `lambda` (constant) such that `f^2(x)=(f^-1(x))^2-lambdaxf(x)f^-1(x)+3x^2f(x)` where all x`in R^+`

Text Solution

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As `f(x)=f^(-1)(x)=x`
`f(f(x))=x`
so,`x^2=x^2-lambda .x..x+3x^2.x`
=`0=x^2(-lambda+3)`
`lambda=3`
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