Question #dc53c

2 Answers
Jul 28, 2017

Visualize the function and determine the values that alter the range.

Explanation:

The range of a function is different for each function.

The best way (in my opinion) is to visualize the function on a graph. This includes considering all values that change the range. For example, the #c#-value.

Let's use an example of a quadratic function.

If we have a quadratic function of #f(x) = 3(4-x)^2+3# shown here:

graph{3(4-x)^2+3 [-14.24, 14.24, -7.11, 7.13]}

We can look at the #c#-value and determine all possible values the function can have as the #f# variable.

In this case, it's any value equal to or greater than #3#.

Thus, our range is #{y in RR| y>=3}#

In conclusion, recognize which variables change the range, and visualize the function. It becomes much easier to determine the range.

Hope this helps :)

Jul 28, 2017

Find the domain of the inverse.

Explanation:

The domain of a function #f(x)# is equal to the range of its inverse #f^-1(x)#. Similarly, the range of a function #f(x)# is equal to the domain of its inverse #f^-1(x)#.