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Vesna [10]
3 years ago
7

What is the inverse of the function g(x)=x^3/8+16

Mathematics
1 answer:
shtirl [24]3 years ago
7 0

Answer:

The inverse of the function is f^{-1}(x) = \sqrt[3]{\frac{x-16}{8}}

Step-by-step explanation:

Inverse of a function:

Suppose we have a function y = g(x). To find the inverse, we exchange the values of x and y, and then isolate y.

In this question:

y = \frac{x^3}{8} + 16

Exchanging x and y:

x = \frac{y^3}{8} + 16

\frac{y^3}{8} = x - 16

y^3 = \frac{x-16}{8}

y = \sqrt[3]{\frac{x-16}{8}}

The inverse of the function is f^{-1}(x) = \sqrt[3]{\frac{x-16}{8}}

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