Question

Find the domain and y interceptF(x) = 5 + x/4 - x

Answer 1

`f(x)=(5+x)/(4-x)`

First we will calculate the domain of the function, for this we have to see in what value is indeterminate to exclude it from the domain of the reals. That is, we will make the denominator equal to zero and we will find the values to exclude:

`\begin{gathered} 4-x=0 \\ x=4 \end{gathered}`

Then the domain will be all reals minus x = 4

`(-\infty,4)\cup(4,\infty)\to\text{Domine}`

To find the intercepts of the function we must make them both zero:

For the y-intercept:

`\begin{gathered} x=0 \\ f(0)=(5+0)/(4-0) \\ f(0)=(5)/(4)\to y-intercept \end{gathered}`

For the x-intercept:

`\begin{gathered} y=0=f(x) \\ (5+x)/(4-x)=0 \\ 5+x=0 \\ x=-5\to x-\text{intercept} \end{gathered}`