Can you explain why f(x) does not equal -1? I followed the math that Greg did on the top right but don’t understand the reasoning.
Because f(x) cannot take the value of -1.
If you try solving the equation,
3 - x / x - 2 = -1,
you’ll get
3 - x = -x + 2
Which comes to 3 = 2?? which is not true
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Thanks! Can we identify this by just looking at the function ? or do we have to always solve?
One way is to test with a very large number, but often just looking at the question or (in this case) a bit of algebra is enough. The way to formally show that the range cannot be -1 is to split the fraction:
\frac{3 - x}{x - 2} = \frac{(2 - x) + 1}{x - 2} = - 1 + \frac{1}{x - 2} \neq -1
as \frac{1}{x - 2} must equal something.
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