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If a < 0,="" the="" function="" f(x)="eax" +="" e-="" ax="" is="" a="" monotonically="" decreasing="" function="" for="" values="" of="" />
given by :
  • a)
    x > 0
  • b)
    x < />
  • c)
    x > 1
  • d)
    x < />
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
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="" />< />
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Most Upvoted Answer
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).
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If a given by :a)x > 0b)x c)x > 1d)x Correct answer is option 'B'. Can you explain this answer?
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