What would the inverse equation be?

Question

The equation is 3^x+5 and have to find the inverse :(

p.s is this possible on graphing calculators?

Answer 1

y = 3^x+5

 

If you graph this function (by hand or on a graphing calculator) you will see that the graph is increasing.  So the function satisfies the Horizontal Line Test (i.e., it is one to one).  Therefore, the function has an inverse function.  

 

To find the inverse function, switch x and y and then solve for y.

 

Switch x and y:  x = 3^y + 5

 

Solve for y:  3^y = x-5

 

                log₃(3^y) = log₃(x-5)

 

                        y = log₃(x-5)

 

As far as graphing is concerned, you can obtain the graph of the inverse function by reflecting the graph of the original function in the line

y = x. 

 

 

Answer 2

When finding the inverse of a function, you switch the y and x spots.

 

y= 3^x+5

 

x= 3^y+5     when moving the variable out of the exponent, use Ln

 

lnx = ln3^y+5    Using the properties you can then move the

                      exponents in front of the Ln.

 

lnx = (y+5)ln3   Then divide both sides by ln3 and they cancel.

ln3           ln3          

 

lnx = y+5          Then subtract 5 on both sides.

ln3

 

lnx - 5  =  y^{-1       This is the inverse of the function.}

ln3

 

Graphing calculators, depends on which one you have.  But usually you can google it for the specific one you have.