How do you find the inverse of $f(x)=3x^4$ ?

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Answer 1 · 2018-04-05T12:57:10

$f^-1(x) = + root(4)(x/3)$

$f(x)=3x^4 ; x>=0$
$y=3x^4$
$x=3y^4$
$y^4=x/3$
$y= root(4)(x/3)$
$f^-1(x) = + root(4)(x/3)$

Note: in the case of $f(x) = 3x^4$ there are two values of $x$ that

give the same $f(x)$ . This is because both $f(x) = x^4$ and also

$f(−x) = x^4$ . We cannot define $f^-1$ of something to be two

different things. So we restrict the domain of the function for

$x>=0$

graph{3x^4 [-10, 10, -5, 5]} [Ans]

How do you find the inverse of f(x)=3x^4f(x)=3x^4?