Question

For f(x)= `ℓn|x + sqrt(x^2 + 1)|`, then the value of`g(x) = (cosx)^((cosecx - 1))` and `h(x) = (e^x - e^-x)/(e^x + e^-x)`, then the value of `|(f(0), f(e), g(π/6)),(f(-e), h(0), h(π)),(g((5π)/6), h(-π), f(f(f(0))))|` is ______.

Options

• 0.00

• 1.00

• 2.00

• 3.00

Answer 1

For f(x)= `ℓn|x + sqrt(x^2 + 1)|`, then the value of`g(x) = (cosx)^((cosecx - 1))` and `h(x) = (e^x - e^-x)/(e^x + e^-x)`, then the value of `|(f(0), f(e), g(π/6)),(f(-e), h(0), h(π)),(g((5π)/6), h(-π), f(f(f(0))))|` is 0.00.

Explanation:

∵ `f(0) = 0, f(-e) = -f(e), g((5π)/6) = -g(π/6)`

`h(-π) = -h(π), h(0)` = 0

∴ Determinant value is zero.