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How do you simplify and list the restrictions for #h (x)= (7 - x) /( 3x - 21)#?

Answer 1

Ethan Adkins

Refer to explanation

We have that

#3x-21=0=>x=7# hence the domain is #R-{3}#

we have that

#h(x)=(7-x)/(3(x-7))=-1/3#

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Answer 2

Jace Anderson

To simplify and list the restrictions for the function h(x) = (7 - x) / (3x - 21), we can follow these steps:

Simplify the expression: h(x) = (7 - x) / (3x - 21) Simplify the numerator: 7 - x Simplify the denominator: 3x - 21 Simplify further: 7 - x / 3(x - 7)
List the restrictions: To find the restrictions, we need to identify any values of x that would make the denominator equal to zero, as division by zero is undefined. Set the denominator equal to zero and solve for x: 3x - 21 = 0 3x = 21 x = 7

Therefore, the restriction for h(x) is x ≠ 7.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.