Algebraic fractions and binary operations

Question 1 of 10

If a ⊕ b = a² − ab, evaluate 2 ⊕ 2.

Question 2 of 10

2/x × x/4 = 1/2 for x ≠ 0.

Question 3 of 10

If a * b = a + b + 4 on the real numbers, find the identity element.

Question 4 of 10

A binary operation * is defined on the real numbers by a * b = a + b + 4ab. (a) Show that * is commutative. (b) Find the identity element. (c) Find the inverse of 4 under *.

Question 5 of 10

If x * y = xy − x, then 4 * 4 = ___

Question 6 of 10

The identity element under multiplication is 1.

Question 7 of 10

A binary operation * is associative if

Question 8 of 10

If a ⊕ b = a² − ab, evaluate 5 ⊕ 5.

Question 9 of 10

If x * y = xy − x, then 7 * 4 = ___

Question 10 of 10

A binary operation * is defined on the real numbers by a * b = a + b + 4ab. (a) Show that * is commutative. (b) Find the identity element. (c) Find the inverse of 3 under *.