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๐‘“(๐‘ฅ)=4๐‘ฅ+7f(x)=4x+7. Find the inverse of f(x).A.๐‘“โˆ’1(๐‘ฅ)=๐‘ฅโˆ’74f โˆ’1 (x)= 4xโˆ’7โ€‹ B.๐‘“โˆ’1(๐‘ฅ)=7โˆ’4๐‘ฅf โˆ’1 (x)=7โˆ’4xC.๐‘“โˆ’1(๐‘ฅ)=4๐‘ฅโˆ’7f โˆ’1 (x)=4xโˆ’7D.๐‘“โˆ’1(๐‘ฅ)=๐‘ฅโˆ’47f โˆ’1 (x)= 7xโˆ’4โ€‹ SUBMITarrow_backPREVIOUS

Question

๐‘“(๐‘ฅ)=4๐‘ฅ+7f(x)=4x+7. Find the inverse of f(x).A.๐‘“โˆ’1(๐‘ฅ)=๐‘ฅโˆ’74f โˆ’1 (x)= 4xโˆ’7โ€‹ B.๐‘“โˆ’1(๐‘ฅ)=7โˆ’4๐‘ฅf โˆ’1 (x)=7โˆ’4xC.๐‘“โˆ’1(๐‘ฅ)=4๐‘ฅโˆ’7f โˆ’1 (x)=4xโˆ’7D.๐‘“โˆ’1(๐‘ฅ)=๐‘ฅโˆ’47f โˆ’1 (x)= 7xโˆ’4โ€‹ SUBMITarrow_backPREVIOUS

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Solution

To find the inverse of the function f(x) = 4x + 7, we need to follow these steps:

  1. Replace f(x) with y, so the equation becomes y = 4x + 7.
  2. Swap x and y to get x = 4y + 7.
  3. Solve the equation for y to find the inverse function.

Subtract 7 from both sides: x - 7 = 4y. Then divide both sides by 4: (x - 7) / 4 = y.

So, the inverse function is f^(-1)(x) = (x - 7) / 4.

Therefore, the correct answer is A. f^(-1)(x) = (x - 7) / 4.

This problem has been solved

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