How do you find the inverse of $f (x) = x^{3} - 2$ $f(x)=x^3-2$ and is it a function?

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How do you find the inverse of $f (x) = x^{3} - 2$ $f(x)=x^3-2$ and is it a function?

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Answer 1 · 2016-03-16T22:31:05

$f^{- 1} (x) = 0^{3} \sqrt{x} + 2$ $f^-1(x)=color(white)(0)^3sqrtx+2$

Explanation:

We begin with $f (x) = x^{3} - 2$ $f(x)=x^3-2$ . To find the inverse of any equation, just switch $x$ $x$ and $y$ $y$ . No, before we do thta, I'm going to change the equation. I'm going to rename $f (x)$ $f(x)$ to $y$ $y$ , just so that I don't have to deal with the parentheses or anything. Now, all I'bve doe is change what $f (x)$ $f(x)$ is called, not it's actual value.

Anyways, we have $y = x^{3} - 2$ $y=x^3-2$ . Now we switch $x$ $x$ and $y$ $y$ and then solve for $y$ $y$ .

Now we've got $x = y^{3} - 2$ $x=y^3-2$ . If we add $2$ $2$ on both sides we have $x + 2 = y^{3}$ $x+2=y^3$ . Now we just need to get $y$ $y$ as simple as possible, which we'll do by cube rooting both sides of the equation. That leaves us with $y = 0^{3} \sqrt{x} + 2$ $y=color(white)(0)^3sqrtx+2$ . Now we just change $y$ $y$ back to $f (x)$ $f(x)$ and add a $0^{- 1}$ $color(white)(0)^-1$ to write it in inverse notation, and we have $f^{- 1} (x) = 0^{3} \sqrt{x} + 2$ $f^-1(x)=color(white)(0)^3sqrtx+2$ .

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How do you find the inverse of $f (x) = x^{3} - 2$ $f(x)=x^3-2$ and is it a function?

1 Answer

Explanation:

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How do you find the inverse of f(x)=x^3-2f(x)=x3−2f(x)=x^3-2 and is it a function?

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How do you find the inverse of $f (x) = x^{3} - 2$ $f(x)=x^3-2$ and is it a function?