Find the inverse function of f
F(x)=under root 2+6x then find
F inverse of (x)= ;x>equal to 0
To find the inverse of f(x) = √(2 + 6x), we will switch the x and y variables and solve for y.
Let y = √(2 + 6x)
Now, solving for x:
x = √(2 + 6y)
Squaring both sides to eliminate the square root:
x^2 = 2 + 6y
Rearranging the equation:
6y = x^2 - 2
Dividing both sides by 6:
y = (x^2 - 2) / 6
Therefore, the inverse function of f(x) = √(2 + 6x) is:
F^(-1)(x) = (x^2 - 2) / 6
To find the inverse function of f(x) = √(2+6x), we need to switch the roles of x and y and solve for y.
Step 1: Replace f(x) with y.
y = √(2+6x)
Step 2: Swap x and y.
x = √(2 + 6y)
Step 3: Solve for y.
Square both sides to get rid of the square root.
x^2 = 2 + 6y
Step 4: Rearrange the equation to solve for y.
6y = x^2 - 2
y = (x^2 - 2) / 6
Therefore, the inverse function of f(x) = √(2+6x) is f^(-1)(x) = (x^2 - 2) / 6.
To find the inverse function of f(x) = √(2 + 6x), we need to follow these steps:
Step 1: Replace f(x) with y:
y = √(2 + 6x)
Step 2: Swap x and y:
x = √(2 + 6y)
Step 3: Solve for y:
x^2 = 2 + 6y
Step 4: Move 2 to the other side of the equation:
6y = x^2 - 2
Step 5: Divide the entire equation by 6:
y = (x^2 - 2) / 6
Step 6: Replace y with f^(-1)(x):
f^(-1)(x) = (x^2 - 2) / 6
Therefore, the inverse function of f(x) = √(2 + 6x) is f^(-1)(x) = (x^2 - 2) / 6.
Now, to find f^(-1)(x), given that x ≥ 0:
We can directly substitute x into the inverse function:
f^(-1)(x) = (x^2 - 2) / 6
For x ≥ 0, we simply replace x with the given value.
Therefore, f^(-1)(x) = (0^2 - 2) / 6 = -2/6 = -1/3.