Question

Use the functions given by f(x) = (-x/8)+1 and g(x) = x^3 to find (f o g)^-1 (-5).

Answer 1

well what is your fog? Did you do that first

Answer 2

I am stuck between (f(g(x)))^-1 or (f^-1(g^-1(x)))

Answer 3

Of course they are asking the first one
But firstly, did you find f(g(x))

Answer 4

Isn't it: (f(g(x)))^-1 = (f(x^3))^-1 = (((-x^3)/8)+1)^1

Answer 5

why are you doing it that way! you are mixing things that should not be mixed
First find fog! forgot about inverse thing for a moment
get the function.

Answer 6

(f o g) = [(-x^3)/8] +1

Answer 7

Good!
Now since that function is 1 to 1
then it has an inverse
let's call that function h(x)=(fog)(x)
from inverse property we now that if \(h^-1(-5)=a,~ then~ h(a)=-5\)
then we have \(\Large\frac{-a^3}{8}+1=-5\)
solve for a

Answer 8

know that*

Answer 9

that's \(h^{-1}(-5)=a\) in 4th line (correction)

Answer 10

So, (-x^3)/8 = -6
-x^3 = -48
x^3 = 48
x = cube root of 48

Answer 11

yes! simplify that more

Answer 12

I mean x is a,
and a = 2 * cube root of 6

Answer 13

that's okay a or x doesn't matter, it's just a matter of choosing a variable
so now we go back to our line above
we said \(h^{-1}(-5)=a\\ so~~ h^{-1}(-5)=2\sqrt[3]{6}\)

Answer 14

and our h^-1(x) is just (fog)^-1(x)
as we set it

Answer 15

Ok, this makes so much more sense now! Thank you for all of your help.

Answer 16

welcome^_^