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$Given the function $f(x)=3x^3+2$, find the value of $x$ so that $f^{-1}(x)=4$.$

Guest Nov 11, 2014

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$Given the function $f(x)=3x^3+2$, find the value of $x$ so that $f^{-1}(x)=4$.$

If the inverse returns 4, then the original function substitutes 4 for x

So we have

3(4)³ + 2 = 3*64 + 2 = 194 and that's "x" in the inverse

So (4, 194) is on the original graph and (194, 4) is on the inverse

CPhill Nov 11, 2014

CPhill · Answer 1 · 2014-11-11T04:11:14

$Given the function $f(x)=3x^3+2$, find the value of $x$ so that $f^{-1}(x)=4$.$

If the inverse returns 4, then the original function substitutes 4 for x

So we have

3(4)³ + 2 = 3*64 + 2 = 194 and that's "x" in the inverse

So (4, 194) is on the original graph and (194, 4) is on the inverse