Answer: [tex]f^{-1}(x)\text{ = -}\frac{1}{3}x\text{ + }\frac{4}{3}\text{ \lparen third option\rparen}[/tex]
Explanation:
Given:
f(x) = -3x + 4
To find:
the inverse of the function
To determine the inverse, let y = -3x + 4
interchange x and y:
[tex]x\text{ = -3y + 4}[/tex]
Solve for y by making it the subject of formula:
[tex]\begin{gathered} subtract\text{ 4 from both sides:} \\ x\text{ - 4 = -3y + 4 - 4} \\ x\text{ - 4 = -3y} \end{gathered}[/tex]
divide both sides by -3:
[tex]\begin{gathered} \frac{x\text{ - 4}}{-3}\text{ = }\frac{-3y}{-3} \\ y\text{ = }\frac{x\text{ - 4}}{-3} \\ y\text{ = }\frac{x}{-3}\text{ -}\frac{4}{-3} \end{gathered}[/tex][tex]\begin{gathered} y\text{ = }\frac{-x}{3}\text{ + }\frac{4}{3} \\ \\ y\text{ = -}\frac{1}{3}x\text{ + }\frac{4}{3}\text{ } \\ \\ f^{-1}(x)\text{ = -}\frac{1}{3}x\text{ + }\frac{4}{3}\text{ \lparen third option\rparen} \end{gathered}[/tex]
