๐(๐ฅ)=4๐ฅ+7f(x)=4x+7. Find the inverse of f(x).A.๐โ1(๐ฅ)=๐ฅโ74f โ1 (x)= 4xโ7โ B.๐โ1(๐ฅ)=7โ4๐ฅf โ1 (x)=7โ4xC.๐โ1(๐ฅ)=4๐ฅโ7f โ1 (x)=4xโ7D.๐โ1(๐ฅ)=๐ฅโ47f โ1 (x)= 7xโ4โ SUBMITarrow_backPREVIOUS
Question
๐(๐ฅ)=4๐ฅ+7f(x)=4x+7. Find the inverse of f(x).A.๐โ1(๐ฅ)=๐ฅโ74f โ1 (x)= 4xโ7โ B.๐โ1(๐ฅ)=7โ4๐ฅf โ1 (x)=7โ4xC.๐โ1(๐ฅ)=4๐ฅโ7f โ1 (x)=4xโ7D.๐โ1(๐ฅ)=๐ฅโ47f โ1 (x)= 7xโ4โ SUBMITarrow_backPREVIOUS
Solution
To find the inverse of the function f(x) = 4x + 7, we need to follow these steps:
- Replace f(x) with y, so the equation becomes y = 4x + 7.
- Swap x and y to get x = 4y + 7.
- 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.
Similar Questions
Select the correct answer.What is the inverse of function f?๐โก(๐ฅ)=๐ฅ+7 A. ๐-1โก(๐ฅ)=(๐ฅ+7)2,for๐ฅโฅ-7 B. ๐-1โก(๐ฅ)=๐ฅ2+7,for๐ฅโฅ-7 C. ๐-1โก(๐ฅ)=๐ฅ2โ7,for๐ฅโฅ7 D. ๐-1โก(๐ฅ)=(๐ฅโ7)2,for๐ฅโฅ7
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
f(x) = x โ 2. Find the inverse of f(x).A.๐โ1(๐ฅ)=๐ฅโ2f โ1 (x)=xโ2B.๐โ1(๐ฅ)=2๐ฅf โ1 (x)=2xC.๐โ1(๐ฅ)=๐ฅ+2f โ1 (x)=x+2D.๐โ1(๐ฅ)=2โ๐ฅf โ1 (x)=2โx
Find the inverse mentally.f (x) = 7x - 8
If g(x)= ๐ฅ๐ฅ+1x+1xโ then the inverse function g - 1(x) =A.๐ฅ+1๐ฅxx+1โ B.xC.๐ฅ1โ๐ฅ1โxxโ D.๐ฅโ1๐ฅxxโ1โ E.๐ฅ๐ฅ+1x+1xโ SUBMITarrow_backPREVIOUS
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