MATHEMATICS

JAMB 2007 - Question 23

Mathematics 2007 JAMB Past Questions - Question 23: 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 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:
B:
C:
D:
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Correct Answer

B

Explanation

a∆b = a+b+1 → a+a¯¹ = e → 7 +a ¯¹ + 1 =-1 a¯¹ =-1-8 → a¯¹ = -9 To find the inverse of the real number 7 under the binary operation &, we need to find another real number x such that 7 & x = -1, where -1 is the identity element.Using the definition of the binary operation &, we have:7 & x = 7 + x + 1To find the inverse, we need to solve the equation:7 + x + 1 = -1Simplifying the equation:x + 8 = -1Subtracting 8 from both sides:x = -1 - 8x = -9Therefore, the inverse of the real number 7 under the operation & is -9.