Given the function:
[tex]f(x)=x^2+5x-1[/tex]
Let's select the answer for the graph of the function and its inverse.
Let's find random points on the function.
When x = 0:
[tex]f(0)=0^2+5(0)-1=-1[/tex]
When x = -6:
[tex]f(-6)=-6^2+5(-6)-1=36-30-1=5[/tex]
Thus, we have the points:
(x, y) ==> (0, -1) and (-6, 5)
Now, the inverse of this function will contain the points:
(x, y) ==> (-1, 0) and (5, -6)
Where f(x) is the blue function.
From the graphs shown, the graph which contains the points for f(x) = (0, -1) and (-6, 5) and g(x) = (-1, 0) and (5, -6) is the first graph.
Therefore, the correct graph which shows the f(x) and its inverse is:
