Question

Some values for the Range of the rational function f(x) = (3x ^ 2 - 5)/x are undefined, -2, and 10.75. Find the Domain corresponding to each value.
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Answer 1

Answer:

b.{-3,-5,-19}

Step-by-step explanation:

3(-3)²-5=22 and soon

Answer 2

Given: The range of the rational function f(x) = (3x² - 5)/x are

(1) undefined

(2) -2

(3) 10.75

To find: The domain corresponding to each value.

Solution:

• The domain of a function is the value input in place of x.
• The range of a function is the value output after the calculation of f(x) with a particular domain.

(1)

• For the range to be undefined, the domain must be zero.
• Any number divided by zero is undefined.
• Since x is in the denominator, the range would be zero.

(2)

• For the range to be -2, the domain can be calculated as,

       $-2 = \frac{3x^{2} -5} {x}$

        $3x^{2} +2x - 5 = 0$

        $x = 1$ or $x = -\frac{5}{3}$

• So, the domain for the range -2 is 1 or -5/3.

(3)

• For the range to be 10.75, the domain can be calculated as,

        $10.75 = \frac{3x^{2} -5} {x}$

        $60x^{2} -215x-100 = 0$

        $x = 4$ or $x = -\frac{5}{12}$

• So, the domain for the range 10.75 is 4 or -5/12.

Therefore, the domain corresponding to each value is

(1) 0

(2) 1 or -5/3

(3) 4 or -5/12