Open study

is now brainly

With Brainly you can:

  • Get homework help from millions of students and moderators
  • Learn how to solve problems with step-by-step explanations
  • Share your knowledge and earn points by helping other students
  • Learn anywhere, anytime with the Brainly app!

A community for students.

Confirm that f and g are inverses by showing that f(g(x)) = x and g(f(x)) = x. f(x) = x^3 + 4 and g(x) = cube root of (x-4)

See more answers at
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

Get this expert

answer on brainly


Get your free account and access expert answers to this and thousands of other questions

So, first try f(g(x)), this means put the result of function g in function f:\[f(g(x))=\left( \sqrt[3]{x-4} \right)^3+4=...\]Can you see what the next step is?
no. :(
What is the definition of the 3rd root of a number?

Not the answer you are looking for?

Search for more explanations.

Ask your own question

Other answers:

The number whose cube is equal to a given number
OK, but not only a given number, but the number from which you wanted to know the 3rd root: e.g: the 3rd root of 8 is 2, because: 2^3=8. So: the 3rd root of x-4 is p, then p³=x-4. So...\[(\sqrt[3]{x-4})^3=x-4\]by definition.
so that will get the expression out from under the radical
so i'll get x-4+4
or x-8
@ZeHanz am i correct?
You get x-4+4=x in my book...
oh srry
So we've done the first half of the proof. Now the second: put the result of f in g:\[g(f(x))=\sqrt[3]{x^3+4-4}\]
ok. thnx. but where did u get p from?
p is not important. You can name it anyway you want. Just look at it this way: say you've got a terribly complex expression, such as:\[3x^{23}-5x^{16}+\frac{ 1 }{ 2x }\] First, they want you to calculate the 3rd root of it. I really don't know what it would be, so let's call it p for now:\[p=\sqrt[3]{3x^{23}-5x^{16}+\frac{ 1 }{ 2x }}\]Looks awful, not? Now you have to calculate .... p³. Well, you don't have to think long about it, youve got your original complex expression back! The reason for this, that the 3rd root and the 3rd power are each other's inverse. This means: they undo each other's effect on numbers you put in!

Not the answer you are looking for?

Search for more explanations.

Ask your own question