Find the Function g(x)=3x

$g (x) = 3 x$

The function $G (x)$ can be found by evaluating the indefinite integral of the derivative $g (x)$ .

$G (x) = \int g (x) d x$

Since $3$ is constant with respect to $x$ , move $3$ out of the integral.

$3 \int x d x$

By the Power Rule, the integral of $x$ with respect to $x$ is $\frac{1}{2} x^{2}$ .

$3 (\frac{1}{2} x^{2} + C)$

Simplify the answer.

Rewrite $3 (\frac{1}{2} x^{2} + C)$ as $3 (\frac{1}{2}) x^{2} + C$ .

$3 (\frac{1}{2}) x^{2} + C$

Combine $3$ and $\frac{1}{2}$ .

$\frac{3}{2} x^{2} + C$

The function $G$ if derived from the integral of the derivative of the function. This is valid by the fundamental theorem of calculus.

$G (x) = \frac{3}{2} x^{2} + C$