Question

please explain why the function with the equation **(given below) is not defined for x<0.

Answer 1

\[f(x)=\sin(\cos ^{-1}x)\]

Answer 2

Because an inverse is a function only if the original is a one-to-one (injective) function. The cosine function must be restricted so that it behaves as an injective function. Thus the restricted cosine function f(x) = cos x must have a domain 0 ≤ x ≤ π.

Answer 3

So I assume you understand?

Answer 4

YUP! thank you so much! i knew the reason but i could not think when i read the question.. thank you again!

Answer 5

Welcome anytime!