challenge #2\nfunctions $j(x)$ and $k(x)$ are inverses.\nwhat is an equation for the function $k(x)$?\nuse a…

challenge #2\nfunctions $j(x)$ and $k(x)$ are inverses.\nwhat is an equation for the function $k(x)$?\nuse a sheet of paper if it helps with your thinking.\n$j(x)=4(x - 1)$

challenge #2\nfunctions $j(x)$ and $k(x)$ are inverses.\nwhat is an equation for the function $k(x)$?\nuse a sheet of paper if it helps with your thinking.\n$j(x)=4(x - 1)$

Answer

Explanation:

Step1: Define given function $j(x)$

From the diagram, $j(x) = 4(x - 1)$

Step2: Set $y = j(x)$ to find inverse

Let $y = 4(x - 1)$

Step3: Swap $x$ and $y$ for inverse

$x = 4(y - 1)$

Step4: Solve for $y$ (isolate $y$)

First, divide both sides by 4: $\frac{x}{4} = y - 1$ Then add 1 to both sides: $y = \frac{x}{4} + 1$

Step5: Rename $y$ as $k(x)$

Since $k(x)$ is the inverse of $j(x)$, $k(x) = \frac{x}{4} + 1$

Answer:

$k(x) = \frac{x}{4} + 1$