Sketching Graphs (1 Viewer)

[xwrathbringerx]

If f(x) = x^2 – 6x + 5, sketch a graph of the region defined by the intersection of the inequalities f(x) + f(y) ≤ 0 and f(x) – f(y) ≥ 0.

How on earth do I do this

 

[Trebla]

If f(x) = x^2 – 6x + 5, sketch a graph of the region defined by the intersection of the inequalities f(x) + f(y) ≤ 0 and f(x) – f(y) ≥ 0.

How on earth do I do this

f(x) = x² - 6x + 5
f(y) = y² - 6y + 5

i.e.
y = x² - 6x + 5
x = y² - 6y + 5

f(x) and f(y) are inverses of each other. Once you know how to sketch y = f(x), you can easily sketch the inverse and eventually the regions f(x) ≤ - f(y) and f(x) ≥ f(y)

 

[xwrathbringerx]

What R the regions f(x) ≤ - f(y) and f(x) ≥ f(y)