Question

Given f(x) =

Answer 1

The end behavior of the given function (range) is x< 4 or x > 4. So, f(x) < 4 or f(x) > 4. The solution in interval notation is $\mathbf{(-\infty, 4) \cup (4, \infty)}$.

The last option is correct.

What is the range of the function?

The end behavior of the given function f(x) = (8x+1)/2x-9 wants us to identify the range of the given function.

The range is the set of values of the dependent variable for which a function is defined. The function range is the combined domain of the inverse function.

From the information given:

$\mathbf{f(x) = \dfrac{8x +1}{2x -9 }}$

Inverse of $\mathbf{\dfrac{8x +1}{2x -9 }}$ becomes $\mathbf{f(x) = \dfrac{1+9x}{2(-4+x) }}$

The domain of the inverse is x< 4 or x > 4. So, f(x) < 4 or f(x) > 4. Now, representing the solution in interval notation, we have:

$\mathbf{(-\infty, 4) \cup (4, \infty)}$

Learn more about the range of a given function here:

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