Is $f (x) = 3 x^{- 2} - 3$ $f(x)=3x^-2 -3$ a function?

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Is $f (x) = 3 x^{- 2} - 3$ $f(x)=3x^-2 -3$ a function?

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Answer 1 · 2018-03-07T08:35:56

We can rewrite $f (x)$ $f(x)$ as $f (x) = \frac{3}{x^{2}} - 3$ $f(x)=3/x^2-3$ . For this equation to be a function, one value of $x$ $x$ must not give more than one value for $y$ $y$ , so each $x$ $x$ value has a unique $y$ $y$ value. Also, every value for $x$ $x$ must have a value for $y$ $y$ .

In this case, each value for $x$ $x$ has one value for $y$ $y$ . However, $x \neq 0$ $x!=0$ since $f (0) = \frac{3}{0} - 3 = undefined$ $f(0)=3/0-3="undefined"$ .

So, $f (x)$ $f(x)$ is not a function.

However, it can be made a function by applying limits or ranges of $x$ $x$ values, in this case it is a function if $f (x) = 3 x^{- 2} - 3, x \neq 0$ $f(x)=3x^-2-3,x!=0$ .

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Is $f (x) = 3 x^{- 2} - 3$ $f(x)=3x^-2 -3$ a function?

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