Question

explain the relationship between the exponential function f(x) = 2^x+1 and it's inverse?


urgent.. exam tomorrow D:

Answer 1

@sourwing @phi please?

Answer 2

\[
y=2^x+1\\
y=\frac{\ln (x-1)}{\ln (2)}
\]
They are symmetric with the line y=x

Answer 3

See the graphs

Answer 4

i need a detailed explanation D: and I'm not allowed to use my calc for such sections ;_;

Answer 5

Try to fill in the details. Do you know how to find the inverse of a function?

Answer 6

f(x)=(2^x) +1
f(x)-1=2^x
apply log in base e
ln [f(x)-1] =ln(2^x)
ln [f(x)-1] =xln2

{1/[f(x)-1]}f'(x)=ln2
f'(x)=ln2 [f(x)-1]
f'(x)=ln2[2^x +1-1]
f'(x)=ln2(2^x

Answer 7

f(x)= 2^x+1
let y be the image of x under 'f'
so, y= 2^x+1
now, we need to interchange the values of x and y,,
in this way:
x=2^y+1
or, x-1=2^y
or, (root over) x-1 = y
hence, f inverse (x) = (root over) x-1