ANSWER
[tex]y = 3x[/tex]
EXPLANATION
The given function is
[tex]f(x) = {x}^{2} + x + 1[/tex]
To find the gradient function, we find the first derivative;
[tex]f'(x) = 2x+ 1[/tex]
To find the gradient at (1,3), we put x=1 into the gradient function to get;
[tex]f'(1) = 2(1)+ 1 = 3[/tex]
The equation of the tangent line is
[tex]y-y_1=m(x-x_1)[/tex]
We substitute the point and the slope to get,
[tex]y-3=3(x-1)[/tex]
This simplifies to
[tex]y = 3x - 3 + 3[/tex]
[tex]y = 3x[/tex]
