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!
