For the function f(x)=((x+4))/(7), find f^(-1)(x). f^(-1)(x)=7(x+4) f^(-1)(x)=7(x-4) f^(-1)(x)=(x)/(7)-4 f^(-1)(x)=7x-4

Write original function as y: To find the inverse function, f^(-1)(x), we need to switch the roles of x and y in the original function and then solve for y. The original function is f(x) = (x + 4) / 7, so we start by writing it as y = (x + 4) / 7.Replace y with x: Next, we replace y with x to reflect the inverse relationship: x = (y + 4) / 7.Solve for y: Now, we solve for y by multiplying both sides of the equation by 7 to get rid of the denominator: 7x = y + 4.Isolate y: Finally, we subtract 4 from both sides to isolate y: 7x - 4 = y.Inverse function: Therefore, the inverse function, f^(-1)(x), is f^(-1)(x) = 7x - 4.

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Q. For the function

f(x)=\frac{(x+4)}{7}

, find

f^{-1}(x)

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f^{-1}(x)=7(x+4)

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f^{-1}(x)=7(x-4)

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f^{-1}(x)=\frac{x}{7}-4

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f^{-1}(x)=7 x-4

Write original function as $y$ : To find the inverse function, $f^{-1}(x)$ , we need to switch the roles of $x$ and $y$ in the original function and then solve for $y$ . The original function is $f(x) = \frac{x + 4}{7}$ , so we start by writing it as $y = \frac{x + 4}{7}$ .
Replace $y$ with $x$ : Next, we replace $y$ with $x$ to reflect the inverse relationship: $x = \frac{y + 4}{7}$ .
Solve for y: Now, we solve for $y$ by multiplying both sides of the equation by $7$ to get rid of the denominator: $7x = y + 4$ .
Isolate y: Finally, we subtract $4$ from both sides to isolate $y$ : $7x - 4 = y$ .
Inverse function: Therefore, the inverse function, $f^{-1}(x)$ , is $f^{-1}(x) = 7x - 4$ .