Question

the least integral value in range of f(x) = 3^x + 3^-x is​

Answer 1

Answer:

the answer -3 hop it helps

Answer 2

Answer:

The least integral value is 2.

Step-by-step explanation:

Given: f(x) = $3^{x}+3^{-x}$

Recall: If two positive values a and b are given, then

AM of a and b ≥ GM of a and b

Here a= 3ˣ and b= 3⁻ˣ

Where 3ˣ >0 and 3⁻ˣ > 0 so we can apply AM and GM concept here.

=> AM of 3ˣ and 3⁻ˣ = (3ˣ + 3⁻ˣ)/2

=> GM of 3ˣ and 3⁻ˣ = √(3ˣ × 3⁻ˣ) = 1

∵ AM ≥ GM

∴ (3ˣ + 3⁻ˣ)/2 ≥ 1

⇒ 3ˣ + 3⁻ˣ ≥ 2

Hence, the range of the function f(x) = 3ˣ + 3⁻ˣ is [2 , ∞) i.e; least integral value is 2.

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