Answer
$f(x)=-\frac{1}{2}x+4$.
Work Step by Step
The given point is $(2,3)$.
The given equation is $y=2x-3$.
The equation is in slope intercept form $y=mx+b$.
The slope $m=2$.
The slope of the perpendicular line is the negative reciprocal of $m=2$.
Thus, the slope of the required line is $m_1=-\frac{1}{2}$.
The point is $(x_1,y_1)=(2,3)$.
The equation of the line passes through the point $(x_1,y_1)$ and the slope $m_1=-\frac{1}{2}$ is.
$\Rightarrow y-y_1=m(x-x_1)$
Substitute all values into the above equation.
$\Rightarrow y-3=-\frac{1}{2}(x-2)$
Apply the distributive property.
$\Rightarrow y-3=-\frac{1}{2}x+1$
Add $3$ to both sides.
$\Rightarrow y-3+3=-\frac{1}{2}x+1+3$
Simplify.
$\Rightarrow y=-\frac{1}{2}x+4$
Let $y=f(x)$.
$\Rightarrow f(x)=-\frac{1}{2}x+4$.
