Respuesta :

sir05
the inverse graph should be on the other side of the Y=X line therefore the inverse graph can be found by swapping the X coordinates and Y coordinates so the inverse graph should go through the points (-2,0) and (0,5)
calculista

Answer:

[tex]f^{-1}(x)=\frac{5}{2}x+5[/tex]

Step-by-step explanation:

step 1

Find the equation of the graph

Let

[tex]A(0,-2), B(5,0)[/tex]

The slope of the linear equation is equal to

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

substitute the values

[tex]m=\frac{0+2}{5-0}[/tex]

[tex]m=\frac{2}{5}[/tex]

The equation of the line into point-slope form is equal to

[tex]y-y1=m(x-x1)[/tex]

substitute

[tex]y-0=\frac{2}{5}(x-5)[/tex]

[tex]y=\frac{2}{5}x-2[/tex] --------> linear equation of the graph

Step 2

Find the inverse function

Exchanges the variables x for y and y for x

[tex]x=\frac{2}{5}y-2[/tex]

Isolate the variable y

[tex]y=\frac{5}{2}x+5[/tex]

Let

[tex]f^{-1}(x)=y[/tex]

[tex]f^{-1}(x)=\frac{5}{2}x+5[/tex] --------> inverse of the function of the graph