Question

Algebra function problem?
Given the following function h(x) = √(2-3x)

a. Determine h(x-1)

b.Determine the implied domain of h(x-1). Expressed in interval notation.

Answer 1

h(x) = √(2 - 3x)

a). Determine h(x - 1) = √[2 - 3(x - 1)]

h(x - 1) = √[2 - 3x + 3)]

h(x - 1) = √(5 - 3x)

 

b). Determine the implied domain of h(x-1)

Implied domain:

If the test or your instructor only states the rule for a function, then the domain will be implied. That domain is the largest set of real numbers that can be used in that rule.

Domain of h(x - 1) is h(x)

h(x) = √(2 - 3x) has the implied domain of R - real smaller then 2/3 or all x ≥ 2/3 or  {x|x ≥ 2/3}.

Comments

• b).

The radical function is h(x - 1) = √(5 - 3x)

Domain: The domain of a function is the set of all possible input values (often the "x" variable), which produce a valid output from a particular function. It is the set of all real numbers for which a function is mathematically defined

Domain of a function f(x) is set of those values of x which will make the function mathematically legal or correct.. certain operations like division by zero , square root of a negative number do not exist in real maths.

5 - 3x ≥ 0

5 ≥ 3x

5/3 ≥ x

⇒ x  ≤ 5/3.

So, the domain of the above function is all non negative real numbers. those less than or equal to 5/3.

Implied domain of h(x - 1) = √(5 - 3x) is { x ∈ R : x ≤ 5/3 }.

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Implied domain of h(x - 1) = √(5 - 3x) is { x ∈ R : x ≤ 5/3 }.

The interval notation form of domain of h(x - 1) = √(5 - 3x) is (- ∞, 5/3].