Solving functions algebraically (cube roots)

[KatieLynn]

Homework Statement

Show f and g are inverse functions or state that they are not.
f(x)= cube root of -8x-6 g(x)= -(x^3+6)/(8)

Homework Equations

You find inverses by plugging the equations into each other, if they are inverses then once you simplify the composed equation, it will equal x.

The Attempt at a Solution

cube root of {-8[-(x^3+6)/(8)]-6} I plugged g(x) into f(x) now I need to solve it, this is what I did but its not right because the answer should come out to be just x.

I multiplied everything by 8 to get it out of the denominator and simplified the numerator which left me with

cube root of {64x^3-432}

then I thought maybe you could pull out the 64 and x^3 from the cube root to get

4x times the cube root of {-432}

which is definitely not going to = x not matter what I do to it.

I feel a bit stupid for not being able to solve this because the solving is not supposed to be the challenge, the concept of what makes the functions of inverses is. I think I've just forgotten how to solve harder equations.

 

[danago]

I think its just a case of a mistake in your algebra. Can you show your full working perhaps?

 

[EnumaElish]

Say f(x) = y = cube root of -8x-6.

Solve for [EDIT: x].

Hint: y^3 = -8x-6.

Replace x with y, and y with x. Check to see y = g(x).

 

[HallsofIvy]

Homework Statement

Show f and g are inverse functions or state that they are not.
f(x)= cube root of -8x-6 g(x)= -(x^3+6)/(8)

Homework Equations

You find inverses by plugging the equations into each other, if they are inverses then once you simplify the composed equation, it will equal x.

The Attempt at a Solution

cube root of {-8[-(x^3+6)/(8)]-6} I plugged g(x) into f(x) now I need to solve it, this is what I did but its not right because the answer should come out to be just x.

I multiplied everything by 8 to get it out of the denominator and simplified the numerator which left me with

cube root of {64x^3-432}

You multiplied everything by 8? Wouldn't it be easier just to cancel the "8" in the numerator with the "8" in the denominator?