Questions: Let f(x)=15x+14 f^(-1)(x)=

Transcript text: Let $f(x)=15 x+14$ \[ f^{-1}(x)= \]

Solution

Step 1: Define the Function

We start with the function defined as: \[ f(x) = 15x + 14 \]

Step 2: Set Up the Inverse

To find the inverse function $ f^{-1}(x) $, we swap $ x $ and $ f(x) $: \[ x = 15y + 14 \]

Step 3: Solve for $ y $

Next, we isolate $ y $ in the equation: \[ x - 14 = 15y \] \[ y = \frac{x - 14}{15} \]

Thus, the inverse function is: \[ f^{-1}(x) = \frac{x - 14}{15} \]

The inverse function is given by: \[ \boxed{f^{-1}(x) = \frac{x - 14}{15}} \]

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