Mathematics

A binary operation Δ is defined by aΔb = a + b + 1 for…

A binary operation Δ is defined by aΔb = a + b + 1 for any numbers a and b. Find the inverse of the real number 7 under the operation Δ, if the identity element is -1
  • A.
    -7
  • B.
    -9
  • C.
    5
  • D.
    9
Correct Answer: Option B
Explanation

a*e = a + e + 1 = a
implies e+ 1 = 0
∴ e = -1
7 * e = -1
∴ a + 7 + 1 = -1
a + 8 = -1
a+8 = -1
a = -1-8
a = -9