## CarlyLiberty 2 years ago Find the Inverse of the function: f(x)= (x/6)^3 - 7 My answer was f^-1(x) = 6(x+7)^3 is this correct?

1. freewilly922

You exponent is incorrect.

2. CarlyLiberty

so would i write it like this? f^-1(x) = [6(x+7)]3

3. CarlyLiberty

ohhh or is it f^-1(x) = 6(x^3 + 7)?

4. freewilly922

No, what you did wrong was to assume that $(y/6)^3 =x+7 \to y/6=(x+7)^3$ That's not how you get rid of exponents. if $y^4=x\to y=x^{1/4}$

5. CarlyLiberty

okay, so it should be f-1(x) = 18(x + 7) then? Thats the only other answer i got...

6. freewilly922

You first answer was correct EXCEPT the actual number you put in the exponent. if you had $y=(x/2)^3-1$ then to find the inverse swap x and y and solve $x=(y/2)^3-1$ then $x+1=(y/2)^3$ this is where you did something weird. Where I would take the 1/3 root of both sides: $(x+2)^{1/3} = ((y/2)^3)^{\frac{1}{3}}=y$ you took both sides to the third power.

7. CarlyLiberty

Oh okay, i see what i types wrong...thank you so much!

8. freewilly922

Good luck!