Determine algebraically whether f(x)=3x-2 and g(x)=(x+2)/3 are inverse functions. Show all work.

Yes

Step-by-step explanation:

f(x)=3 x-2      

y= 3 x-2      

x= 3y - 2  

3 y -2 = x

3 y -2 + 2 = x + 2

3 y =  x   +  2                                                      

3        3       3

3 y =  x   +  2                                                      

3        3       3

y =  x  +  2          replace y with f ^ -1(x)

     3        3                                            

f ^-1 (x) =    x   +  2        

                 3       3      

linear pair postulates

b. 6

step-by-step explanation:

we are given the table representing an exponential function.

we can see from the table that, as x is increasing, the value of y is increasing in the power of 6.

i.e. the following relation is obtained,

x = 1, y = 6

x = 2, y = 36 =

x = 3, y = 216 =

x = 4, y = 1296 =

x = 5, y = 7776 =

so, the geometric series obtained is .

thus, the common ratio is given by = = 6.

hence, the common ratio is 6.