Given the functions k(x) = 2x2 − 5 and p(x) = x − 3, find (k ∘ p)(x).
(k ∘ p)(x) = 2x2 − 6x + 4
(k ∘ p)(x) = 2x2 − 12x + 13
(k ∘ p)(x) = 2x2 − 12x + 18
(k ∘ p)(x) = 2x2 − 8

guess at question:

a vertical line intersects the graph of g(x,y) = 0 at two points. what conclusion follows about the function f(x) implicitly defined by g(x,f(x)) = 0?

the domain of f(x) cannot include the x coordinate of any such vertical line.

informally, f(x) is not a function, and

g(x,y)=0 cannot be solved for y uniquely.

the relation r = {(x,y) such that g(x,y) = 0} is a function if

for all (a,b) ∊ r and (c,d) ∊ r, a=c implies b=d.

step-by-step explanation:

answer:   (s+1)(s+4)

step-by-step explanation:

factor s2+5s+4

s2+5s+4

=(s+1)(s+4)