If a given by :a)x > 0b)x c)x > 1d)x Correct answer is option 'B'. Ca...
f(x) = eax + e- ax
But a < />
∴ e ax - e - ax > 0
⇒ e ax > e - ax
⇒ ax > - ax ⇒ 2 ax > 0
∴ ax > 0, then x < 0="" (∴="" a="" />< />
If a given by :a)x > 0b)x c)x > 1d)x Correct answer is option 'B'. Ca...
**Explanation:**
To determine the correct answer, we need to analyze the given conditions:
a) x > 0: This condition states that x is a positive number.
b) x < 1:="" this="" condition="" states="" that="" x="" is="" less="" than="" />
c) x > 1: This condition states that x is greater than 1.
d) x: This condition states that x can take any value.
From the given conditions, we can see that option B, x < 1,="" satisfies="" both="" conditions="" b)="" and="" c).="" let's="" break="" down="" each="" condition="" and="" understand="" why="" option="" b="" is="" the="" correct="" />
**Condition a) x > 0:**
This condition indicates that x is a positive number. However, option B does not violate this condition since x can be any value less than 1, including positive values.
**Condition b) x < />
This condition states that x is less than 1. Option B satisfies this condition, as it explicitly states that x is less than 1.
**Condition c) x > 1:**
This condition states that x is greater than 1. Option B violates this condition since x is less than 1. Therefore, option B is not the correct answer based on this condition.
**Condition d) x:**
This condition states that x can take any value. Option B satisfies this condition since x can be any value less than 1.
Considering all the conditions, option B is the correct answer because it satisfies conditions a) and b) while also satisfying condition d). However, it does not satisfy condition c).
In conclusion, option B is the correct answer because it satisfies the given conditions a), b), and d) while violating condition c).