Confirm that f and g are inverses by showing that f(g(x)) = x and g(f(x)) = x.

f(x) = x3 + 4 and g(x) = Cube root of quantity x minus four.

Question

Confirm that f and g are inverses by showing that f(g(x)) = x and g(f(x)) = x.

f(x) = x3 + 4 and g(x) = Cube root of quantity x minus four.

mertsj · Answer

Did you find f(g(x)) ?

anonymous · Answer

No?

hero · Answer

Writing it out makes no clear distinction on whether g(x) is $\sqrt[3]{x-4}$ or $\sqrt[3]{x} - 4$

hero · Answer

If you don't know how to use latex, just simply write something like cbrt(x) - 4 or 
cbrt(x - 4)

mertsj · Answer

$$f(x)=x^3+4$$
$$g(x)=\sqrt[3]{x-4}$$

mertsj · Answer

$$f(g(x))=(\sqrt[3]{x-4})^3+4=(x-4)+4=x$$

mertsj · Answer

Do you understand that?

anonymous · Answer

My bad its cbrt (x-4)

mertsj · Answer

Do you know that the cube root and the third root is the same thing?

anonymous · Answer

yes

mertsj · Answer

So, therefore, what I wrote is correct.

anonymous · Answer

Yes no im not saying that it isn't I was replying to Hero. Sorry! And as far as understanding I am pretty sure you plugged in g(x) into f(x) but Im having troubles understanding where you plugged It in

mertsj · Answer

If a problem says to find the f(3) that means to take the function f and replace every x with a 3.   Do you understand that?

anonymous · Answer

Yes

anonymous · Answer

Oh Im sorry I see it now! It just takes me a while..

mertsj · Answer

So if a problem (such as yours) says to find the f(g(x)) that means to take the function f and replace every x with g(x)

mertsj · Answer

So:
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