Solve g(x2)=g(x)-6: Functions Problem Homework

[Kushal]

Homework Statement

part of the question is:

g:x = b - $$\sqrt[3]{x}$$

x is real

Solve g(x²) = g(x) - 6

Show that:

g(x⁶) + 4g(x³) $$\leq$$ 5b + 4 for all real values of x

The Attempt at a Solution

If i at least have a hint on how to start the first part i guess i'll be able to do the second one...

thank you!

 

[Kushal]

errmmm it's been solved...

it was as simple as replacing the x in g(x) by x²

thanks anyway

 

[HallsofIvy]

Homework Statement

part of the question is:

g:x = b - $$\sqrt[3]{x}$$

Do you mean g(x)= b- $$\sqrt[3]{x}$$?

x is real

Solve g(x²) = g(x) - 6

Well, what is g(x²)? You are given the formula for g(x), just put x² in place of x.

Show that:

g(x⁶) + 4g(x³) $$\leq$$ 5b + 4 for all real values of x

The Attempt at a Solution

If i at least have a hint on how to start the first part i guess i'll be able to do the second one...

thank you!

What are g(x⁶) and g(x³)? Again, just replace x in the formula for g(x) by the appropriate thing.