Find the domain of the function hx x 4x3 49x fx xSquarer

Find the domain of the function. h(x) = x - 4/x^3 - 49x f(x) = x/Squareroot 3x - 10 Use the factor Theorem to determine whether x - c is a factor of f(x). 5x^4 + 9x^3 - 2x^2 + 2; x + 2 Solve the inequality. Graph the solution set. |3x - 7| + 5 greaterthanorequalto 13 Determine the end behavior for the following function: f(x) = -x^2 (x + 6)^3 (x^2 - 1) polynomial, list each real zero and its multiplicity. Determine intercept. f(x) = 2(x + 5)(x - 3)^4 f(x) = x^2(x^2 - 4)(x + 4) Given zero to find the remaining zeros of the function. f(x) = x^3 - 3x^2 - 5x + 39; zero: -3

Solution

1. h(x) = (x-4)/(x³-49x)

In a rational expression denominator cant be zero. So we have to check out which value of x makes the denominator zero

x³-49x=0

x(x²-49)=0

x=0,49

Therefore the domain is (-infinity,0)U(0,49)U(49,infinity)

2. f(x)=x/sqrt(3x-10)

The denominator cant be zero and square root cant take negative terms

sqrt(3x-10)>0

3x-10>0

x>10/3

Therefore the domain is (10/3,infinity)