Question #d5779

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Answer 1 · 2017-04-05T00:13:32

Substitute $f^-1(x)$ for x
Use the property $f(f^-1(x)) = x$
Solve for $f^-1(x)$

Given: $f(x) = root3(x/7) -9$

Substitute $f^-1(x)$ for every x:

$f(f^-1(x)) = root3(f^-1(x)/7) -9$

Use the property $f(f^-1(x)) =x$ :

$x= root3(f^-1(x)/7) -9$

Add 9 to both sides:

$x+9= root3(f^-1(x)/7)$

Cube both sides:

$(x+9)^3= f^-1(x)/7$

Multipy both sides by 7:

$f^-1(x)=7(x+9)^3$