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๐‘“(๐‘ฅ)=5๐‘ฅ+3f(x)=5x+3. Find the inverse of f(x).A.๐‘“โˆ’1(๐‘ฅ)=3โˆ’5๐‘ฅf โˆ’1 (x)=3โˆ’5xB.๐‘“โˆ’1(๐‘ฅ)=๐‘ฅโˆ’53f โˆ’1 (x)= 3xโˆ’5โ€‹ C.๐‘“โˆ’1(๐‘ฅ)=๐‘ฅโˆ’35f โˆ’1 (x)= 5xโˆ’3โ€‹ D.๐‘“โˆ’1(๐‘ฅ)=5๐‘ฅโˆ’3f โˆ’1 (x)=5xโˆ’3SUBMITarrow_backPREVIOUS

Question

๐‘“(๐‘ฅ)=5๐‘ฅ+3f(x)=5x+3. Find the inverse of f(x).A.๐‘“โˆ’1(๐‘ฅ)=3โˆ’5๐‘ฅf โˆ’1 (x)=3โˆ’5xB.๐‘“โˆ’1(๐‘ฅ)=๐‘ฅโˆ’53f โˆ’1 (x)= 3xโˆ’5โ€‹ C.๐‘“โˆ’1(๐‘ฅ)=๐‘ฅโˆ’35f โˆ’1 (x)= 5xโˆ’3โ€‹ D.๐‘“โˆ’1(๐‘ฅ)=5๐‘ฅโˆ’3f โˆ’1 (x)=5xโˆ’3SUBMITarrow_backPREVIOUS

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Solution

To find the inverse of the function f(x) = 5x + 3, we follow these steps:

  1. Replace f(x) with y, so the equation becomes y = 5x + 3.
  2. Swap x and y to get x = 5y + 3.
  3. Solve for y to find the inverse function.

Subtract 3 from both sides: x - 3 = 5y. Then divide both sides by 5: (x - 3) / 5 = y.

So, the inverse function is f^(-1)(x) = (x - 3) / 5.

Therefore, the correct answer is B. f^(-1)(x) = (x - 3) / 5.

This problem has been solved

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