Question

g

Answer 1

"x^2 - x - 12.3 = 0

x = 5.35, x = 4.03"

you calculated zero points for the function. using quadratic root formula. So at these points the function is zero.
Do we know, from this, values left and right of the poles though?

Answer 2

x = 4.03 is probably
δ away from x.....

in this case, the maximum error is achieved... and you get a root...

5.35.....that is far right...it's a "coincidence" that f(x)-L<ε there...
f(x) is not the same as L because it is inside its limiting variables,
but because the function goes through y=5 again...

Answer 3

"|(x^2 - x - 7) - 5| < 0.3" try to factor the function to |x+ | |x- |.
Then the bigger bracket is the limiting condition...