Question 7
Find the inverse of $f (x) = \frac{- 3 x - 2}{4 x + 1}$
$f^{- 1} (x) =$
Question Help: DVideo Message instructor
Submit Question Jump to Answer

Answer

Expert–verified

Hide Steps

Answer

$f^{- 1} (x) = \frac{- 4 x - 2}{3 x + 1}$ is the final answer.

Steps

Step 1 ：The problem is asking for the inverse of the function $f (x) = \frac{- 3 x - 2}{4 x + 1}$ .

Step 2 ：To find the inverse of a function, we need to switch the roles of $x$ and $y$ and solve for $y$ .

Step 3 ：Let's start by replacing $f (x)$ with $y$ , so we have $y = \frac{- 3 x - 2}{4 x + 1}$ .

Step 4 ：Next, we swap $x$ and $y$ to get $x = \frac{- 3 y - 2}{4 y + 1}$ .

Step 5 ：Now, we solve for $y$ to get the inverse function. We can do this by multiplying both sides by $4 y + 1$ and then adding 2 to both sides and dividing by -3.

Step 6 ：This gives us the inverse function $f^{- 1} (x) = \frac{- 4 x - 2}{3 x + 1}$ .

Step 7 ： $f^{- 1} (x) = \frac{- 4 x - 2}{3 x + 1}$ is the final answer.

Question 7Find the inverse of f(x)=−3x−24x+1f−1(x)=Question Help: DVideo Message instructorSubmit Question Jump to Answer

Answer

Popular Problems

Question 7
Find the inverse of $f (x) = \frac{- 3 x - 2}{4 x + 1}$
$f^{- 1} (x) =$
Question Help: DVideo Message instructor
Submit Question Jump to Answer