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Answer the following question based on the information given below.
For three distinct real numbers $x, y$ and $z,$ let

• $f(x, y, z) = \min(\max(x, y), \max(y, z), \max(z, x))$
• $g(x, y, z) = \max(\min(x, y), \min(y, z), \min(z, x))$
• $h(x, y, z) = \max(\max(x, y), \max(y, z), \max(z, x))$
• $j(x, y, z) = \min(\min(x, y), \min(y, z), \min(z, x))$
• $m(x, y, z) = \max(x, y, z)$
• $n(x, y, z) = \min(x, y, z)$

Which of the following expressions is necessarily equal to $1?$

1. $(f(x, y, z) – m(x, y, z))/(g(x, y, z) – h(x, y, z))$
2. $(m(x, y, z) – f(x, y, z))/(g(x, y, z) – n(x, y, z))$
3. $(j(x, y, z) – g(x, y, z))/h(x, y, z)$
4. $(f(x, y, z) – h(x, y, z))/f(x, y, z)$

Say (x,y,z)=(1,3,4)

f(x,y,z)=3

g(x,y,z)=3

h(x,y,z)=4

j(x,y,z)=1

Now putting value we get the answer
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### 1 comment

Need to show that other options are false also. Or else, prove f=g and m = h.

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