1) Let's turn them as equations
f(x) = 2x -3 Make f(x) =0
2x -3 =0 Add 3 to both sides
2x = 3 Divide both sides by 2
x=3/2
This is the x-intercept of that function f(x) = 2x -3
As for g(x) = 3x²+3x +7
g(x) = 3x²+3x +7 Make g(x) =0
3x² +3x +7 =0
Let's solve it use the Resolutive Formula for Quadratic Equation
![\begin{gathered} \Delta=(3)^2-4(3)(7)\text{ }\Rightarrow\Delta=-75 \\ x=\frac{-3+-\sqrt[]{-75}}{2(3)} \\ x_1=-(1)/(2)+\frac{5\sqrt[]{3}i}{6} \\ x_2=-(1)/(2)-\frac{5\sqrt[]{3}i}{6} \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/b0gmrnm5skspi75rrr86dkwf5cn9h42i86.png)
So as we can see, the equation has complex roots and therefore the parabola does not intercept the x-axis in any point