+633 I'm assuming f^{-1} is a way of switching the input and output values, which works for this function. Therefore f^{-1}(f(f^{-1(19))) --> f^{-1} = 19, so f(x) = 19. I substituted the equation in and got x^3-8 = 19. I added 8 to each side to get x^3 = 27. To get x without an exponent, I took the cube root of each side, getting x = 3. Either way, f^{-1}(f(f^{-1(19))) = f^{-1}(19) = f(3)
+9466 f( f-1(x) ) = x
Therefore
f( f-1(19) ) = 19
And
f-1( f( f-1(19) ) ) = f-1( 19 )
To find f-1(19) , lets first find f-1(x) .
f(x) = x3 - 8
y = x3 - 8 → y + 8 = x3 → (y + 8)1/3 = x
f-1(x) = (x + 8)1/3 Now plug in 19 into this function.
f-1(19) = (19 + 8)1/3 = 271/3 = 3
