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JAMB Mathematics 2024 Paper

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Question : 46

Total: 50

A binary operation * is defined on a set of real numbers by x*y = x

^y

for all values of x and y, if x * 2 = x, find the possible values of x.

0, 2
1, 2
0, 1
2, 2

Solution:

Concept:

A binary operation defined by

x * y = x^y

is applied with

y = 2

, giving an equation to solve for

x

.

Explanation:

Given

x * y = x^y

, substitute

y = 2

.

Then

x * 2 = x^2

.

The condition states

x * 2 = x

.

So

x^2 = x

.

Bring all terms to one side:

x^2 - x = 0

.

Factorize:

x(x - 1) = 0

.

Thus, either

x = 0

or

x - 1 = 0

, giving

x = 0

or

x = 1

.

Answer:

The possible values of

x

are

0

and

1

.

Correct option: C.

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