Consider the exponential function

MATHEMATICS · Multi-part · CBSE · Mathematics · Continuity and Differentiability · Continuity and Differentiability

Problem

f(x)=2\cdot 3^{x}

. Answer the following briefly, showing adequate reasoning wherever asked: (i) Define an exponential function in the general form

y=a\,b^{x}

, specifying the conditions on

a

and

b

. (ii) State the domain of

f(x)

and explain, in one or two sentences, why this domain holds for every exponential function. (iii) Determine the range of

f(x)

and justify your answer by referring to the sign of the constant

a

and the basic properties of

3^{x}