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What is the domain and range of #g(x) = 1/(7-x)^2#?

Answer 1

Eva Abramson

Domain: #(-oo, 7) uu (7, + oo)#.
Range: #(0, +oo)#

The domain of the function will have to take into account the fact that the denominator cannot be equal to zero.

This means that any value of #x# that will make the denominator equal to zero will be excluded from the domain.

In your case, you have

#(7-x)^2 = 0 implies x = 7#

This means that the domain of the function will be #RR - {7}#, or #(-oo, 7) uu (7, + oo)#.

To find the range of the function, first note that a fractional expression can only be equal to zero if the numerator is equal to zero.

In your case, the numberator is constant and equal to #1#, which means that you cannot find an #x# for which #g(x) = 0#.

Moreover, the denominator will always be positive, since you're dealing with a square. This means that the range of the function will be #(0, +oo)#.

graph{1/(7-x)^2 [-20.28, 20.27, -10.14, 10.12]}

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Answer 2

Nathan Axel

The domain of the function g(x) = 1/(7-x)^2 is all real numbers except x = 7. The range of the function is all real numbers greater than 0.

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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.