Question

# A simplified form of (√3^2x)+2+3^−2x that does not involve radicals or fractional exponents can be obtained after factoring the radicand. Find this si

Transformations of functions

A simplified form of $$(\sqrt{3^2x})+2+3^{−2x}$$ that does not involve radicals or fractional exponents can be obtained after factoring the radicand. Find this simplification.

Multiply the radicand by $$\displaystyle{3}^{{2}}\cdot{x}:$$ $$=\sqrt{((3^2x)+2+3^-2x)*(3^2x)/(3^2x)} =\sqrt{((3^4x)+(2^2x)+(3^0))/(3^2x)}$$
Simplify: $$=\sqrt{(((3^2x)^2)+2(3^2x)+1)/3^2x} =\sqrt{((3^2x)+1)^2}/(3^2x)=\sqrt{((3^2x+1)/3^x)^2} =((3^2x)+1)/(3^x)\ or\ 3^x +3^{-x}$$