Let f(x) = x^2 - x + k - 2,k in R. Then the c | vedclass

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(D) The function $y = |f(|x|)|$ is non-derivable at $5$ points if the quadratic equation $x^2 - x + k - 2 = 0$ has two distinct positive roots.For the

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$(2, 9/4)$

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(D) The function $y = |f(|x|)|$ is non-derivable at $5$ points if the quadratic equation $x^2 - x + k - 2 = 0$ has two distinct positive roots.For the roots to be real and distinct,the discriminant $D > 0$:$D = (-1)^2 - 4(1)(k - 2) > 0$$1 - 4k + 8 > 0$$9 - 4k > 0 \Rightarrow k For the roots to be positive,the product of roots $\alpha\beta > 0$ and the sum of roots $\alpha + \beta > 0$:Product $\alpha\beta = k - 2 > 0 \Rightarrow k > 2$.Sum $\alpha + \beta = 1 > 0$ (which is always true).Combining these conditions,we get $2 Thus,the set of values is $(2, 9/4)$.

Let $f(x) = x^2 - x + k - 2$,$k \in R$. Then the complete set of values of $k$ for which $y = |f(|x|)|$ is non-derivable at $5$ distinct points is:

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