state the domain of each function: 1. f(x)= 2x+1/x^2-1 2. f(x)=x√2x-5 3. f(x)= 4x-1/√16-x^2

Answer 1

1.

f(x) = (2x+1)/(x²-1) = (2x+1)/(x+1)(x-1)

The domain are all real numbers, except 1 and -1.

That is because x=1 and x=-1 make the denominator 0.

2.

f(x) = x √(2x-5)

The domain is x ≥ 2.5, because those values make 2x-5 ≥ 0.

3.

f(x) = (4x-1)/√(16-x²)

The domain are all the x satisfying -4 < x < 4.

It is only the values in the interval (-4,4) that make 16-x1.

f(x) = (2x+1)/(x²-1) = (2x+1)/(x+1)(x-1)

The domain are all real numbers, except 1 and -1.

That is because x=1 and x=-1 make the denominator 0.

2.

f(x) = x sqrt(2x-5)

The domain is x >=2.5, because those values make 2x-5 >= 0.

3.

f(x) = (4x-1)/sqrt(16-x²)

The domain are all the x satisfying -4 < x < 4.

It is only the values in the interval (-4,4) that make 16-x² > 0