p(5)* Define T: P2 → R² by T(p) Find a non-trivial element of the kernel. .P(6). p(t)

consider the statement (formula) (3x)A(x) → A(z) where z is a new variable not free (not an "input variable") in A(x). Find now a specific example of A(x) over the set N and choose a specific value of z N so that (1) becomes false (meaning we cannot prove it, since proofs start from true axioms and preserve truth at every step). (1)

3 Let f(x)=(x-1)², g(x)=x², and E= {x:-8≤x≤8}. Find the inverse image (gof)¹(E).

t5 (t + 8) ¹ (t + 2)¹ (t + 7)* t³ (t + 8)^(t + 7)³ (t-6) ²² Given g(t) = Round all answers to 3 decimal places as needed. If the answer doesn't exist, type DNE. answer the following questions: a) The domain of g in set notation and interval notation is: Set Notation: {t | t is a real number and t + Interval Notation: b) The t-intercept(s) are: c) The vertical asymptotes of g are at t Write the answer(s) as just numbers separated by commas. d) g has a hole at the ordered pair: Write each hole as an ordered pair. Do not do any rounding until the final answer. e) The g(t)-intercept is: f) The end behavior of g is: RH: As LH: As ↑ ↑ ↑ ↑ Horizontal Asymptote: Write the horizontal asymptote as y = # if it exists. If it doesn't exist, type DNE.