SOLUTION: Re: Simplifying Rational Expressions and Functions
I understand how to write a function in simplified form using factoring and removing the factor = to 1. However, can someone wal
Question 359121: Re: Simplifying Rational Expressions and Functions
I understand how to write a function in simplified form using factoring and removing the factor = to 1. However, can someone walk me through the steps on determining the restrictions on the domain? I can't figure out how the restrictions on the domain are determined.
Write the function given by
g(x)= x^2+3x-10 / 2x^2-3x-2
in simplified form, and list all the restrictions on the domain.
Answer: g(x)= x+5/2x+1, x cannot = -1/2 and x cannot = 2
Please teach me how to determine the restrictions. Thank you. Jill Found 2 solutions by stanbon, ewatrrr:Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website! Write the function given by
g(x)= x^2+3x-10 / 2x^2-3x-2
in simplified form, and list all the restrictions on the domain.
Answer: g(x)= x+5/2x+1, x cannot = -1/2 and x cannot = 2
Please teach me how to determine the restrictions.
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1st: Factor numerator and denominator if you can.
[(x+5)(x-2)]/[(2x+1)(x-2)]
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2nd: The function has a hole at x = 2 because you have
the factor (x-2) in the numerator and in the denominator.
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3rd: The function is undefined at x = -1/2 because the
factor (2x+1) is zero if x = -1/2.
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Comment: As you get further into algebra you will run
into Domain restrictions for two additional reasons:
a) Ex: y = sqrt(x+2)
Since x+2 must not be negative, x must be >= -2.
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b) Ex: y = log(x+2)
Since x+2 must be positive, x must be > -2.
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Cheers,
Stan H. Answer by ewatrrr(24785) (Show Source): You can put this solution on YOUR website!
Hi,
*Note: restrictions on the domain are the values of x that cannot be used.
(those that would make the denominator zero, cannot be used, for ex)
This tells us the denominator would be zero if x = (-1/2) or x = 2
Now Simplifying further: