Operation F means “take the square root,” operation G means “multiply
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29 Jan 2022, 20:41
Positive integer \(x\)
Operation \(F\) - Square root \(= \sqrt{x}\)
Operation \(G\) - multiply by \(c\) \(= cx\)
Operation \(H\) - reciprocal \(= \frac{1}{x}\)
For example,
\(H(G(F(x)) = \frac{1}{c\sqrt{x}}\)
\(H(F(G(x)) = \frac{1}{\sqrt{cx}}\)
For both of these to remains the same, let's compare them
\(\frac{1}{c\sqrt{x}} = \frac{1}{\sqrt{cx}}\)
\(c = \sqrt{c}\)
\(c\) can be \(0\) or \(1\)
But \(c\) can't be \(0\) as the reciprocal will be undefined.
\(c = 1\)
Answer E