Question

Question #dc53c

Answer 1

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 :)

Answer 2

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)`.