Question

f(x)=(x-3)² and g(x)= (5-x)² what is the domain and range​

Answer 1

The domain corresponds to all valid x-values for the equation. Since this is a quadratic equation (highest degree is 2) all x-values are valid.

Domain: {x∈ℝ}

I’d like to point out that this equation is written in vertex form. Vertex formula is written as the following:

y = a(x - h)^2 + k, where (h, k) is the vertex.

y = -(x + 3)^2 + 5, where (-3, 5) is the vertex.

Answer 2

In f(x) = 5-(x+3)²= -x²-6x-4 , x has no impediment in the Real scale so the domain must be all Real x. In the range we see that for f(x)=0 there are the real roots x=-(6±√20)/2 and just as with the domain no reason to except any Real numbers in the range either, now we check for maxima and/or minnima f'(x)=-2x-6 and when x=-3 and f(x)=5 there's a maximum so the domain in the positive scale is conditioned to f(x)≤5