Let f′(x2)=1x for x>0, f(1)=1 and g′(sin2x−1)=cos2x+p for all x� – InterviewSolution

1.	Let f′(x2)=1x for x>0, f(1)=1 and g′(sin2x−1)=cos2x+p for all x∈R, g(−1)=0. If h(x)={f(x),x>0g(x),−1≤x≤0 is a continuous function, then the absolute value of 2p is
Answer» Let $f^{'} (x^{2}) = \frac{1}{x}$ for $x > 0,$ $f (1) = 1$ and $g^{'} ({sin}^{2} x - 1) = {cos}^{2} x + p$ for all $x \in R,$ $g (- 1) = 0.$ If $h (x) = {\begin{matrix} f (x), & x > 0 g (x), & - 1 \leq x \leq 0 \end{matrix}$ is a continuous function, then the absolute value of $2 p$ is

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