can you help me find the inverse of this function algebraically please?
f(x) = 2x^3 + 1
f-1 = 2x^3
(f-1)/2 = x^3
x = ∛((f-1)/2)
so,
f^-1(x) = ∛((x-1)/2)
to find the inverse of a function, rewrite it in the form
y = .....
interchange the x and y variable,
then solve this new equation for y
so
y = 2x^3 + 1
inverse: x = 2y^3 + 1
2y^3 = x - 1
y^3 = (x - 1)/2
y = ( (x-1)/2 )^(1/3)
check with a given point,
in original let x = 3 , y = 2(27) + 1 = 55
in inverse let, x = 55 , y = ( (55-1)/2 )^(1/3)
= 27^(1/3) = 3
My answer is "more than likely" correct
Sure! To find the inverse of a function algebraically, we need to switch the roles of x and y and solve for y. Let's start by replacing f(x) with y:
y = 2x^3 + 1
Now, we'll swap x and y:
x = 2y^3 + 1
Next, we'll solve this equation for y. Let's follow these steps:
Step 1: Subtract 1 from both sides:
x - 1 = 2y^3
Step 2: Divide both sides by 2:
(x - 1)/2 = y^3
Step 3: Take the cube root of both sides:
∛((x - 1)/2) = y
So, the inverse function is:
f^(-1)(x) = ∛((x - 1)/2)
Remember, the cube root symbol (∛) represents raising a number to the power of 1/3.