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T he range of y=(1)/(x²-25) is all Real numbers except for 0. True False

User Strugee
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False.

To understand why, let's first take a closer look at the function we're considering: y = 1 / (x^2 - 25).

A crucial detail here is what happens when the denominator of the fraction becomes 0, which would occur when x equals 5 or -5. Mathematically, division by zero is undefined; therefore, we cannot allow x to be either -5 or 5.

Now, what happens to the function for all real values of x that are not equal to 5 or -5? You might think that since the numerator of the fraction is a constant (1), the output of the function (y) would always be 0. But actually, the denominator of the fraction (x^2 - 25), can reach any positive real number as x approaches positive or negative infinity, meaning that (y), can approach 0 but will never reach it.

Thus, the function y = 1 / (x^2 - 25) can produce any real number excluding 0 as long as x is not equal to 5 or -5.

As such, the statement that the range of the function y = 1 / (x^2 - 25) is all real numbers except for 0 is false. Instead, the range of the function is all real numbers excluding 0.

User Alex Kovshovik
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