Considering only the principal values of the inverse trigonometric functions, the domain o…

Question

Considering only the principal values of the inverse trigonometric functions, the domain of the function $$f(x)=\cos ^{-1}\left(\frac{x^{2}-4 x+2}{x^{2}+3}\right)$$ is :

Accepted Answer

$$ - 1 \le {{{x^2} - 4x + 2} \over {{x^2} + 3}} \le 1$$

$$ \Rightarrow  - {x^2} - 3 \le {x^2} - 4x + 2 \le {x^2} + 3$$

$$ \Rightarrow 2{x^2} - 4x + 5 \ge 0$$ \& $$ - 4x \le 1$$

$$x \in R$$ \& $$x \ge  - {1 \over 4}$$

So domain is $$\left[ { - {1 \over 4},\infty } \right)$$

Solutions · 1