๐(๐ฅ)=5๐ฅ+3f(x)=5x+3. Find the inverse of f(x).A.๐โ1(๐ฅ)=3โ5๐ฅf โ1 (x)=3โ5xB.๐โ1(๐ฅ)=๐ฅโ53f โ1 (x)= 3xโ5โ C.๐โ1(๐ฅ)=๐ฅโ35f โ1 (x)= 5xโ3โ D.๐โ1(๐ฅ)=5๐ฅโ3f โ1 (x)=5xโ3SUBMITarrow_backPREVIOUS
Question
๐(๐ฅ)=5๐ฅ+3f(x)=5x+3. Find the inverse of f(x).A.๐โ1(๐ฅ)=3โ5๐ฅf โ1 (x)=3โ5xB.๐โ1(๐ฅ)=๐ฅโ53f โ1 (x)= 3xโ5โ C.๐โ1(๐ฅ)=๐ฅโ35f โ1 (x)= 5xโ3โ D.๐โ1(๐ฅ)=5๐ฅโ3f โ1 (x)=5xโ3SUBMITarrow_backPREVIOUS
Solution
To find the inverse of the function f(x) = 5x + 3, we follow these steps:
- Replace f(x) with y, so the equation becomes y = 5x + 3.
- Swap x and y to get x = 5y + 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.
Similar Questions
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