When will the function g(x)=-2x^6-4x^4-5x^2-8 be negative?

g(x) = - 2x^6 - 4x^4 - 5x^2 - 8

= - {2x^6 + 4x^4 + 5x^2 + 8)

2x^6 + 4x^4 + 5x^2 + 8 > 0 for all values of x

Hence g(x) = - (2x^6 + 4x^4 + 5x^2 + 8) < 0 for all values of x

g(x)=-2x^6-4x^4-5x^2-8

Note x^6, x^4 and x^2 a >= 0 for all values of x

so g(x)=-2x^6-4x^4-5x^2-8 if -ve for all x; the coeffs of x terms are -ve

All powers are even. That means the powers of x can't be negative. Since the coefficients are negative, then every term must be either less that or equal to zero, and the constant term is strictly less than zero, so the sum must be negative.

So g(x) < 0 for all x.

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It will be negative for all values of x.

It has a domain (-infinity,-8]

" mike g " meant the RANGE is y ≤ - 8