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The domain of this function would be all values of w for which f is defined. Since a number divided by 0 is not defined, f is not defined when any denominator is 0.
Since 2w-7 is in the denominator to find what values for w are allowed we have to find the values where 2w-7 is not equal to 0.
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Which is any value from negative infinity, up to (but not including) 7/2 then from greater than 7/2's on.
but y equate 2w-7 to 0?
I'm not equating. I'm saying that 2w-7 does NOT equal (\(\ne\)) 0. It's the same as solving for what w is if 2w-7 did equal 0, except that we are finding out what w isn't. That way we know what things we cannot have for w otherwise the denominator will be 0 and that cannot happen because dividing by 0 is not defined.