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

B

Explanation:

Let divide g(x) by f(x)

`\frac{ {x}^(2) - 9 }{2 - x {}^{ (1)/(2) } }`

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

`2 - x {}^{ (1)/(2) } = 0`

`x {}^{ (1)/(2) } = 2`

Square both sides

`x = 4`

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

`2 - √(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