A binary operation \(\ast\) is defined on a set of real numbers by x \(\ast\) y = xy for all real values of x.... Question 15076

A binary operation \(\ast\) is defined on a set of real numbers by x \(\ast\) y = x^y for all real values of x and y. If x \(\ast\) 2 = x. Find the possible values of x

0, 1

1, 2

2, 2

0, 2

Correct answer is A

x \(\ast\) y = x^y

x \(\ast\) 2 = x²

x \(\ast\) 2 = x

∴ x² - x = 0

x(x - 1) = 0

x = 0 or 1

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A binary operation \(\ast\) is defined on a set of real numbers by x \(\ast\) y = xy for all real values of x and y. If x \(\ast\) 2 = x. Find the possible values of x

Aptitude Tests

A binary operation \(\ast\) is defined on a set of real numbers by x \(\ast\) y = x^y for all real values of x and y. If x \(\ast\) 2 = x. Find the possible values of x