Why is b ≠ 1 a condition for f(x) = ab^x?

Question

asked Nov 13, 2021 113k views

1 Answer

Pavlin Petkov · Answer 1 · 2021-11-17T10:47:54+0000

In this case, we hace the following exponential function:

f(x)=ab^x

Where:

$a:Initial \ value \\ \\ b:the \ base$

The base
$b\\eq 1$ because 1 raised to any power leads the result of 1. That is:

$1^2=1 \\ \\ 1^3=1 \\ \\ 1^(√(3))=1 \\ \\ \\ In \ conclusion: \\ \\ 1^(n)=1, \ \text{n any real number}$

If so, then we won't get an exponential function, but a constant function:

f(x)=a