Question

Find all x-intercepts of the following function. Write your answer or answers as

coordinate points. Be sure to select the appropriate number of x-intercepts.
f(x)
3x + 30
25x2 - 49

Answer 1

Given: The function below

`f(x)=(3x+30)/(25x^2-49)`

To determine: All x-intercepts of the given function

The x-intercept is a point where the graph crosses the x-axis

We would substitute the function equal to zero and find the value of x

`\begin{gathered} f(x)=(3x+30)/(25x^2-49),f(x)=0 \\ \text{Therefore} \\ (3x+30)/(25x^2-49)=0 \\ \text{cross}-\text{ multiply} \\ 3x+30=0 \end{gathered}`
`\begin{gathered} 3x=-30 \\ (3x)/(3)=(-30)/(3) \\ x=-10 \end{gathered}`

Therefore, the coordinate of the x-intercept is (-10, 0)