Question

can you help me find the inverse of this function algebraically please?

f(x) = 2x^3 + 1

Answer 1

f-1 = 2x^3
(f-1)/2 = x^3
x = ∛((f-1)/2)

so,

f^-1(x) = ∛((x-1)/2)

Answer 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