Question #2a1a4

1 Answer
Mar 25, 2017

The inverse function is: #g^-1(x)=21/(3-x)-7#. See explanation.

Explanation:

To find the inverse function you have to transform the formula of #g(x)# to calculate the value of #x# in terms of #y#:

#y=(3x)/(x+7)#

#y=(3x+21)/(x+7)-21/(x+7)#

#y=3-21/(x+7)#

#21/(x+7)=3-y#

#1/(x+7)=(3-y)/21#

Now we can change the fractions to their reciprocals so that #x# appears in the numerator:

#x+7=21/(3-y)#

#x=21/(3-y)-7#

Now we can "rename" the argument and the value to write the formula using the standard convention (#x# as the argument and #y# as the function's value)

#y=21/(3-x)-7#

Finally we can write the answer:

#g^-1(x)=21/(3-x)-7#