Question

What is the range of f(x) = 1/x?

Answer 1

The range of $f(x)=\frac{1}{x}$ is all values of x except for 0

Step-by-step explanation:

For a function:

• The domain is the range of the x that are allowed for the function - that means, the set of values of x for which the function is defined
• The range is the set of values of y, i.e. the set of all the values that the function can take

The range of a function is also equal to the domain of the inverse function. Therefore, to solve this problem, we can find the inverse function of $f(x)$ and evaluate its range.

We rewrite the function as

$y=\frac{1}{x}$

Now we swap y with x:

$x=\frac{1}{y}$

And then we have to re-arrange the function to make y the subject; we get:

$y=\frac{1}{x}$

which means that the inverse function is

$f^{-1}(x)=\frac{1}{x}$

We notice that the inverse function is equal to the original function.

We notice also that this function is not defined for $x=0$: this means that the domain of the function is all the values of x, except x=0:

$D(f^{-1}(x)): x\neq 0$

this is the domain of $f^{-1}(x)$, which is equal to the range of $f(x)$: therefore, the range of $f(x)$ is all values of x except for 0.

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