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

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To solve the equation g(x²) = g(x) - 6, substitute x² into the function g(x) = b - ∛x. This leads to the expression g(x²) = b - ∛(x²) and simplifies the problem. For the inequality g(x⁶) + 4g(x³) ≤ 5b + 4, replace x in g(x) with x⁶ and x³ respectively to find the necessary expressions. The key to both parts is correctly substituting the values into the function. Understanding these substitutions is essential for solving the problem.
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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!
 
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errmmm it's been solved...

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

thanks anyway
 


Kushal said:

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.
 

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