What is the solution to the equation f(x)=49? what is the meaning of this solution?

This simply means that the equation of the line is a horizontal line at the appropriate y value, in this case 49.

F(X) = 49
Y = 49.

Draw a horizontal line on the y axis at the 49th number, basically, the X coordinates of all other points, would vary, but the y coordinate is the same for all of them. As the graph continues.

Domain is all real number
Range is not, it would be 49 only.

You would plot 83 on the 83 line and you would plot -113 on the -113 line.