Questions: Determine if the function is even, odd, or neither. G(x) = sqrt(10-x^4)

Solution Steps

To determine if a function is even, odd, or neither, we need to check the symmetry of the function. A function \( f(x) \) is even if \( f(x) = f(-x) \) for all \( x \) in the domain, and it is odd if \( f(-x) = -f(x) \) for all \( x \) in the domain. For the given function \( G(x) = \sqrt{10 - x^4} \), we will compute \( G(-x) \) and compare it with \( G(x) \).

We are given the function \( G(x) = \sqrt{10 - x^4} \). To determine if the function is even, odd, or neither, we need to evaluate \( G(-x) \) and compare it with \( G(x) \).

Substitute \(-x\) into the function: \[ G(-x) = \sqrt{10 - (-x)^4} = \sqrt{10 - x^4} \]

Since \( G(x) = \sqrt{10 - x^4} \) and \( G(-x) = \sqrt{10 - x^4} \), we have: \[ G(x) = G(-x) \] This indicates that the function is even.

Final Answer