The given function is:
[tex]f(x)=x^2-5x+1[/tex]
To find the inverse, first you need to check whether the function is bijective, which means:
1) The function should be one-one.
2) The function shoudl be onto.
Graph the function as shown below:
As seen from the graph, the green curve represents the function.
Now draw horizontal and vertical lines on the function.
If the horizontal lines pass through more than one points which can be clearly seen from the graph, the function is not one-one.
Hence the function is not bijective and therefore the inverse of such function does not exist.
