The range of 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 and evaluate its range.
We rewrite the function as
Now we swap y with x:
And then we have to re-arrange the function to make y the subject; we get:
which means that the inverse function is
We notice that the inverse function is equal to the original function.
We notice also that this function is not defined for : this means that the domain of the function is all the values of x, except x=0:
this is the domain of , which is equal to the range of
: therefore, the range of
is all values of x except for 0.
Learn more about domain and range of a function:
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