Question

question 1-2
write an equation for the inverse of ( g(x) = 3x - 8 ).
\\( \circ \\) ( g^{-1}(x) = 8x - 3 )
\\( \circ \\) ( g^{-1}(x) = \frac{1}{3}x + 8 )
\\( \circ \\) ( g^{-1}(x) = \frac{x + 8}{3} )
\\( \circ \\) ( g^{-1}(x) = x + \frac{8}{3} )

Explanation:

Step1: Let \( y = g(x) = 3x - 8 \)

We start by replacing \( g(x) \) with \( y \) to make it easier to solve for \( x \) in terms of \( y \).

Step2: Solve for \( x \) in terms of \( y \)

First, add 8 to both sides of the equation: \( y + 8 = 3x \). Then, divide both sides by 3: \( x=\frac{y + 8}{3}\).

Step3: Replace \( x \) with \( g^{-1}(x) \) and \( y \) with \( x \)

We interchange \( x \) and \( y \) to get the inverse function. So \( g^{-1}(x)=\frac{x + 8}{3}\).

Answer:

\( g^{-1}(x)=\frac{x + 8}{3} \) (the third option)