Question

Find the domain of the function h(x). Show your work using the equation and write the domain using interval notation. h(x) equals the square root of 7-4x.

a) (-[infinity], 7/4)
b) (-[infinity], 7/4]
c) [7/4, [infinity])
d) [7/4, [infinity])

Answer 1

The domain of the function h(x) is (-∞, 7/4].

Step-by-step explanation:

The function h(x) is defined as the square root of 7-4x. To find the domain of h(x), we need to determine the values of x for which the function is defined. Since we cannot take the square root of a negative number, the expression inside the square root, 7-4x, must be greater than or equal to 0. Solving this inequality, we get 7-4x ≥ 0. Rearranging the inequality, we have -4x ≥ -7. Dividing by -4 (and reversing the inequality sign since we are dividing by a negative number), we get x ≤ 7/4.

Therefore, the domain of the function h(x) is (-∞, 7/4].