Let f(x)={sin⁡x,for x≥01−cos⁡x,for x≤0 and g(x)=ex.f(x) = \begin{cases} \sin x, & \text{for } x \geq 0 \\ 1 - \cos x, & \text{for } x \leq 0 \end{cases} \text{ and } g(x) = e^x.…

Mathematics

Problem

Let f(x)={sin⁡x,for x≥01−cos⁡x,for x≤0 and g(x)=ex.f(x) = \begin{cases} \sin x, & \text{for } x \geq 0 \\ 1 - \cos x, & \text{for } x \leq 0 \end{cases} \text{ and } g(x) = e^x. Then LHD of (g∘f)(g \circ f) at x=0x = 0 is (a) 1 (b) -1 (c) 0 (d) None of these

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