Question

G(x)= 1/7x-1, g^-1(6)

Answer 1

`g^(-1)(6)=49`

Explanation:

Inverse function

Given the function:

`\displaystyle g(x) = (1)/(7)x-1`

Find:
`g^(-1)(6)`

Find the inverse function of g.

`\displaystyle y = (1)/(7)x-1`

Add 1:

`\displaystyle y +1= (1)/(7)x`

Multiply by 7:

`7(y +1)= x`

Swap letters:

`y=7(x+1)`

Call this the inverse function:

`g^(-1)(x)=7(x+1)`

Evaluate at x=6

`g^(-1)(6)=7(6+1)=49`

`\boxed{g^(-1)(6)=49}`