Question

Find the domain of
F(×)= 【√log0.5(x^2 + x + 6)】+ 1/x^2 +2x

Answer 1

Answer:

refer the attachment

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Answer 2

Answer:

The domain of the function F(x) can be written as ( -∞ , ∞ ) - { -2 , 0 }.

Step-by-step explanation:

$F(x)=\sqrt{log_{0.5}(x^2+x+6) }+\frac{1}{x^2+2x}$

In the above equation, for domain calculation,

The part of function inside the square root must be greater than or equal to 0.

$log_{0.5} (x^2+x+6)\geq 0\\x^2+x+6\geq 1\\x^2+x+5\geq0$

Since the above equation is satisfied for all the real values of x so the domain of square-root part is (-∞,∞)

Now solving the other half,

The denominator must not be equal to zero

$x^2+2x\neq 0\\x(x+2)\neq 0$

So x must not be 0 or -2 for the function to exist..

Therefore the domain of the function can be written as ( -∞ , ∞ ) - { -2 , 0 }.