Question

Create a logarithmic function in the form f(x) = log_a(x + b) and find its inverse. Show all of your solution steps to earn full credit. Your answer must include:

• A logarithmic function with a base value for a and a constant value for b
• Steps showing how you found your function's inverse
• The inverse function stated in function notation, f ^-1(x)

Answer 1

$f(x)=log_{a}(x+b)$

Let $a=2, b=1$

$f(x)=log_{2}(x+1)$

let $f(x)=y$

$=>y=log_{2}(x+1)$

$=>2^{y}=x+1$

$=>x=2^{y}-1$

Hence, $f^{-1}(x)=2^{x}-1$