Question

Help with this worksheet due tomorrow, please i need help asap. I think the other ones are wrong i’m not sure.

Answer 1

Answer:

2) f^-1(x) = -2x^3 - 6x^2 - 6x - 2

5) g^-1(x) = -1/5x + 1

6) f^-1(x)= -2x^3 - 1

7) g^-1(x) = 1/3x - 3

8) g^-1(x) = 2(x - 2)/(x - 1)

10) f^-1(x) = -x^5

Step-by-step explanation:

2) f(x) = (-2 - ^3√4x) / 2

y = (-2 - ^3√4x) / 2

x = (-2 - ^3√4y) / 2

2x = -2 - ^3√4y

2x + 2 = -^3√4y

(2x + 2)^3 = (-^3√4y)^3

8x^3 + 24x^2 + 24x + 8 = -4y

y = -2x^3 - 6x^2 - 6x - 2

f^-1(x) = -2x^3 - 6x^2 - 6x - 2

Work for (2x + 2)^3

(2x + 2)(2x + 2)

4x^2 + 4x + 4x + 4

(4x^2 + 8x + 4)(2x +2)

8x^3 + 16x^2 + 8x + 8x^2 + 16x + 8

8x^3 + 24x^2 + 24x + 8 = 4y

5) g(x) = -5x + 5

y = -5x + 5

x = -5y + 5

-5y = x - 5

y = -1/5x + 1

g^-1(x) = -1/5x + 1

6) f(x) = ^3√[(-x - 1) / 2]

y = ^3√[(-x - 1) / 2]

x = ^3√[(-y - 1) / 2]

(x)^3 = (^3√[(-y - 1) / 2])^3

x^3 = (-y - 1) / 2

2x^3 = -y - 1

-y = 2x^3 + 1

y = -2x^3 - 1

f^-1(x) = -2x^3 - 1

7) g(x) = 3x + 9

y = 3x + 9

x = 3y + 9

3y = x - 9

y = 1/3x - 3

g^-1(x) = 1/3x - 3

8) g(x) = -[2/(x-2)] + 1

y = -[2/(x - 2)] + 1

x = -[2/(y - 2)] + 1

x - 1 = -[2/(y -2)]

xy - 2x - y + 2 = -2

xy - y = 2x - 4

y(x - 1) = 2x - 4

y = 2(x - 2)/(x - 1)

g^-1(x) = 2(x - 2)/(x - 1)

(x - 1) (y - 2)

xy - 2x - y + 2

10) f(x) = -^5√x

y = -^5√x

x = -5^√y

(x)^5 = (-5^√y)^5

x^5 = -y

y = -x^5

f^-1(x) = -x^5

Sorry for the long drawn out answers, I thought it might help to show you all of the work! Do you need someone to check the other answers?

1) is correct!

3) is correct, except it's f^-1(x) = -^5√x - 3 ( - negative!!!)

4) is incorrect :(, the correct answer is g^-1(x) = (x - 5)/(x - 2)

9) is correct! :D

I hope this helps!!! Good luck!