For the function f(x)=x13+103

Question

, find f−1(x)
.(1 point)
Responses

f−1(x)=3(x−10)3
f inverse of x is equal to 3 times open paren x minus 10 close paren cubed

f−1(x)=(3x)3−10
f inverse of x is equal to 3 x cubed minus 10

f−1(x)=(3x−10)3
f inverse of x is equal to open paren 3 x minus 10 close paren cubed

f−1(x)=(3(x−10))3

Answer 1

To find the inverse of the function \( f(x) = x^{13} + 10^3 \), we first rewrite the function with a little correction:

Given \( f(x) = x^{13} + 10 \).

Next, we set \( y = f(x) \):

\[ y = x^{13} + 10 \]

Now we solve for \( x \):

\[ y - 10 = x^{13} \]

Taking the 13th root of both sides, we have:

\[ x = (y - 10)^{1/13} \]

Thus, the inverse function \( f^{-1}(y) \) is:

\[ f^{-1}(y) = (y - 10)^{1/13} \]

Now we can express \( f^{-1}(x) \) by replacing \( y \) with \( x \):

\[ f^{-1}(x) = (x - 10)^{1/13} \]

None of the responses given exactly match this, but if we focus on the structure of the inverse function, it can be rewritten in terms of different notations.

However, it looks like there was a misunderstanding of the original function in your message with cubed terms. Would you like to clarify or provide more context?