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Range

The range of ...

Question

The range of the function $f (x) = 5^{x} + 5^{- x} + 5$ for $x \in R$ is

A

[3, \infty)

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B

[5, \infty)

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C

[7, \infty)

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D

(7, \infty)

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Solution

The correct option is C $[7, \infty)$
$f (x) = 5^{x} + 5^{- x} + 5$
We know that, $5^{x} + \frac{1}{5^{x}} \geq 2$
$\Rightarrow 5^{x} + \frac{1}{5^{x}} + 5 \geq 7$

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