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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

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Final answer:

The domain of the function h(x) is the set of all real numbers x such that x is less than or equal to 7/4, expressed in interval notation as (-∞, 7/4].

Step-by-step explanation:

To find the domain of the function h(x) = √(7-4x), we need to consider the values of x for which the expression under the square root is non-negative, since the square root of a negative number is not a real number. Therefore, we must find the values of x such that 7-4x ≥ 0. Solving this inequality gives us:

  • 7 - 4x ≥ 0
  • -4x ≥ -7
  • x ≤ 7/4

The domain of h(x) is all real numbers x such that x ≤ 7/4. In interval notation, this is written as (-∞, 7/4].

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