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vivado [14]
2 years ago
5

Im confused on how to work this out

Mathematics
2 answers:
Anuta_ua [19.1K]2 years ago
6 0

If f^{-1}(x) is the inverse of f(x), then

f\left(f^{-1}(x)\right) = x

Given f(x)=x^3+9, we have

f\left(f^{-1}(x)\right) = \left(f^{-1}(x)\right)^3 + 9 = x

Solve for the inverse :

\left(f^{-1}(x)\right)^3 + 9 = x \\\\ \left(f^{-1}(x)\right)^3 = x-9 \\\\ \boxed{f^{-1}(x) = \sqrt[3]{x-9}}

Your answer is incorrect because it's interpreted as "3 times the square root of (x - 9)", whereas you want to end up with "the cube root of (x - 9)".

Try inserting ∛(<em>x</em> - 9) or (<em>x</em> - 9)^(1/3).

Varvara68 [4.7K]2 years ago
3 0

Answer:

cube root (x-9)

Step-by-step explanation:

You have the right approach, but you wrote 3*square root(x-9)

What you need is cube root (x-9).

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