Question

Question #2a1a4

Answer 1

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`