Hyperbolic functions: find the inverse of arcsinh(x)

The function f(x)=2x/3x-5 is one-to-one. find its inverse and check your answer

To find the inverse we can solve for x to convert it to the dependent variable:










Once their roles have reversed, the resulting expression is the inverse:

To check we take the two appropriate inverses to see if they each recover the input (i.e. x).

Checking...

What is the inverse function of (2x-1)/(x-3)

so the inverse function is:

How do you find the inverse of the function f(x)=2(3^x) ?

so the inverse is:

If y=-7log5(2x), find inverse function.

so the inverse is

Determine if g is the inverse of f. f(x)=3x + 5; g(x)=1/3x - 5/3

yes they are inverses of each other

Find the inverse for a quadratic function

y=(x+3)^2

Not invertible unless we restrict the domain



inverse:
 

If f( x ) = ( x - 2 )^3 , then f^-1 ( x ) =

 
therefore 

Simplify 2^(log2(8))

the two functions are inverses so the result is 8

Find the inverse: f(x)=(3x-8)/(4x+5)

what is the inverse of f(x)=7/(6x-5)

 

then... 
 

 

 

 
and so 

what is the inverse of f(x)= 2x-3

 


 



 


so...