Mathematics

Question

Graph the inverse of the function.
Graph the inverse of the function.

1 Answer

  • Answer:

    The graph of the inverse function is the same that the graph of the original function

    Step-by-step explanation:

    step 1

    Find the equation of the function in the graph

    Let

    f(x) ---> the function in the graph

    we know that

    Is a linear function

    take the points (0,6) and (6,0)

    Find the slope of the linear function

    [tex]m=(0-6)/(6-0)\\m=-1[/tex]

    Find the the equation of the linear function in slope intercept form

    [tex]f(x)=mx+b[/tex]

    we have

    [tex]m=-1[/tex]

    [tex]b=6[/tex] ---> the y-intercept is given

    substitute

    [tex]f(x)=-x+6[/tex]

    step 2

    Find the inverse of the function f(x)

    Let

    y=f(x)

    [tex]y=-x+6[/tex]

    Exchange the variables (x for y and y for x)

    [tex]x=-y+6[/tex]

    Isolate the variable y

    [tex]y=-x+6[/tex]

    Let

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

    [tex]f^{-1}(x)=-x+6[/tex]

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

    In this problem the graph of the inverse function is the same that the graph of the original function

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