Answer:
\(f^{-1}(x)=\frac{5}{2}x+5\)
Step-by-step explanation:
step 1
Find the equation of the graph
Let
\(A(0,-2), B(5,0)\)
The slope of the linear equation is equal to
\(m=\frac{y2-y1}{x2-x1}\)
substitute the values
\(m=\frac{0+2}{5-0}\)
\(m=\frac{2}{5}\)
The equation of the line into point-slope form is equal to
\(y-y1=m(x-x1)\)
substitute
\(y-0=\frac{2}{5}(x-5)\)
\(y=\frac{2}{5}x-2\) --------> linear equation of the graph
Step 2
Find the inverse function
Exchanges the variables x for y and y for x
\(x=\frac{2}{5}y-2\)
Isolate the variable y
\(y=\frac{5}{2}x+5\)
Let
\(f^{-1}(x)=y\)
\(f^{-1}(x)=\frac{5}{2}x+5\) --------> inverse of the function of the graph
