Find the inverse function for f(x)= sqrt2x-6
To find the inverse function of f(x) = sqrt(2x) - 6, we need to switch the variables x and y and solve for y.
So, let's begin by switching the variables:
x = sqrt(2y) - 6
Now, let's isolate the term with the square root:
x + 6 = sqrt(2y)
To remove the square root, we square both sides of the equation:
(x + 6)^2 = (sqrt(2y))^2
Simplifying both sides:
(x + 6)^2 = 2y
Next, we divide both sides by 2:
((x + 6)^2)/2 = y
Thus, the inverse function is given by:
f^(-1)(x) = ((x + 6)^2)/2
To find the inverse function of f(x) = √(2x - 6), we need to interchange the roles of x and f(x) and solve for x.
Step 1: Replace f(x) with y:
y = √(2x - 6)
Step 2: Swap x and y:
x = √(2y - 6)
Step 3: Solve for y:
x = √(2y - 6)
Square both sides to eliminate the square root:
x^2 = 2y - 6
Add 6 to both sides:
x^2 + 6 = 2y
Divide both sides by 2:
y = (x^2 + 6)/2
Step 4: Replace y with the inverse function notation, f^(-1)(x):
f^(-1)(x) = (x^2 + 6)/2
Therefore, the inverse function of f(x) = √(2x - 6) is f^(-1)(x) = (x^2 + 6)/2.
To find the inverse function of f(x) = √(2x - 6), we need to first replace f(x) with y:
y = √(2x - 6)
Step 1: Swap x and y in the equation:
x = √(2y - 6)
Step 2: Solve the equation for y:
Square both sides of the equation to eliminate the square root:
x^2 = 2y - 6
Add 6 to both sides of the equation:
x^2 + 6 = 2y
Divide both sides of the equation by 2:
(x^2 + 6)/2 = y
Step 3: Replace y with f^(-1)(x):
f^(-1)(x) = (x^2 + 6)/2
Therefore, the inverse function of f(x) = √(2x - 6) is f^(-1)(x) = (x^2 + 6)/2.