Question

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

Answer 1

Answer:

$g^{-1}(6)=49$

Step-by-step explanation:

Inverse function

Given the function:

$\displaystyle g(x) = \frac{1}{7}x-1$

Find: $g^{-1}(6)$

Find the inverse function of g.

$\displaystyle y = \frac{1}{7}x-1$

Add 1:

$\displaystyle y +1= \frac{1}{7}x$

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

$g^{-1}(6)=7(6+1)=49$

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