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What is the inverse of the function $f(x)=8x+1$ ?

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Absolute value and opposite integers

Full solution

Q. What is the inverse of the function

f(x)=8x+1

?

Switch Roles and Solve: To find the inverse of the function $f(x) = 8x + 1$ , we need to switch the roles of $x$ and $f(x)$ and then solve for the new $x$ . Let $y = f(x)$ , so we have $y = 8x + 1$ . Now, we replace $y$ with $x$ and $x$ with $y$ to get $x$ $0$ .
Replace Variables and Simplify: Next, we need to solve for $y$ in terms of $x$ . To do this, we will first subtract $1$ from both sides of the equation to isolate the term with $y$ . $x - 1 = 8y + 1 - 1$ $x - 1 = 8y$
Isolate y and Divide: Now, we divide both sides of the equation by $8$ to solve for $y$ . $\newline$ $\frac{x - 1}{8} = \frac{8y}{8}$ $\newline$ $y = \frac{x - 1}{8}$
Final Inverse Function: The function we have now, $y = \frac{x - 1}{8}$ , is the inverse of the original function $f(x) = 8x + 1$ . We can denote the inverse function as $f^{-1}(x)$ . So, $f^{-1}(x) = \frac{x - 1}{8}$ .

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