Exponential functions always have a linear variable as a power of constant base and an increasing monotonic graph. Are these e^√x and e^(x^2+1) functions also exponential functions. What is the unique characteristic for which a function is said exponential and do these functions has the same traits. Why they do not have a monotonic graph? Which e^x has. Do they need to satisfy the pre defining properties an exponential function should satisfy i.e. ( base>0, base must not be 1, and power always belongs to real set (R)). Please clarify over each point.

Jadon Johnson

Jadon Johnson

Answered question

2022-11-06

Exponential functions always have a linear variable as a power of constant base and an increasing monotonic graph. Are these e x and e x functions also exponential functions. What is the unique characteristic for which a function is said exponential and do these functions has the same traits. Why they do not have a monotonic graph? Which e x has. Do they need to satisfy the pre defining properties an exponential function should satisfy i.e. ( base>0, base must not be 1, and power always belongs to real set (R)). Please clarify over each point.

Answer & Explanation

Kristen Garza

Kristen Garza

Beginner2022-11-07Added 13 answers

The functions such as f ( x ) = e x and e x 2 + 1 are composite functions on the form f ( x ) = e g ( x ) . They are not exponential functions according to the above definition, except if g(x)=cx+d with constant c,d .
They are "composite exponential functions"
For example in case of g(x)=ln(x) the fonction f ( x ) = e g ( x ) = x is not an exponential function.

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