58. The range of the expression 2^x + 2^-x + 3^x + 3^-x for x belongs to R, is
i) (-infinity, infinity)
ii) [4, infinity)
iii) (6, infinity)
iv) (8, infinity)

Dear student,

The above given expression  2^x + 2^-x + 3^x + 3^-x
As seen in the above expression, x can take values from $\left(-\infty ,\infty \right)$ 
The above given expression can never have its value in negative because it is a strictly increasing function no matter what is the value of x.
The minimum value that the expression can take is to be decided. When we take value of x=0, 
$$\begin{gathered} 2^0+\frac{1}{2^0}+3^0+\frac{1}{3^0} \\ = 1+1+1+1 \\ =4 \end{gathered}$$
Hence the inly possible answer is $\left(4,\infty \right)$
Option 2
Hope this answer has solved your queries
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