Question

If f(1) = 2 – 2 anid 9(37) and g(x) = x2 – 9, what is the domain of g(x) = f(x)?

Answer 1

Answer:

B

Step-by-step explanation:

Let divide g(x) by f(x)

$\frac{ {x}^{2} - 9 }{2 - x {}^{ \frac{1}{2} } }$

The domain of a rational function cannot equal zero so let set the bottom function to zero.

$2 - x {}^{ \frac{1}{2} } = 0$

$x {}^{ \frac{1}{2} } = 2$

Square both sides

$x = 4$

Also we can simplify the bottom denomiator into a square root function

$2 - \sqrt{x}$

The domain of a square root function is all real number greater than or equal to zero because a square root of a negative number isn't graphable.

So we must find a answer that

• Disincludes 4 from the interval
• Doesnt range in the negative number or infinity)
• Range out in positve infinity
• The answer to that is B