Question

URGENTE, URGENT! I NEED HELP ON THE FOLLOWING PROBLEMS. ALSO ARE MY ANSWERS CORRECT? THANKS

Answer 1

1.
`h(x) = \sqrt[3]{x} - 3`

`y = \sqrt[3]{x} - 3`

`x = \sqrt[3]{y} - 3`

`x + 3 = \sqrt[3]{y}`

`(x + 3)^(3) = y`

`(x + 3)(x + 3)(x + 3) = y`

`(x(x + 3) + 3(x + 3))(x + 3) = y`

`(x(x) + x(3) + 3(x) + 3(3))(x + 3) = y`

`(x^(2) + 3x + 3x + 9)(x + 3) = y`

`(x^(2) + 6x + 9)(x + 3) = y`

`x^(2)(x + 3) + 6x(x + 3) + 9(x + 3) = y`

`x^(2)(x) + x^(2)(3) + 6x(x) + 6x(3) + 9(x) + 9(3) = y`

`x^(3) + 3x^(2) + 6x^(2) + 18x + 9x + 27 = y`

`x^(3) + 9x^(2) + 27x + 27 = y`

`x^(3) + 9x^(2) + 27x + 27 = h^(-1)(x)`

2.
`g(x) = (1)/(x) - 2x`

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

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

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

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

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

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

3.
`f(x) = 4x`

`y = 4x`

`x = 4y`

`(x)/(4) = (4y)/(4)`

`(1)/(4)x = y`

`(1)/(4)x = f^(-1)(x)`

4.
`f(x) = -(1)/(5)x - 1`

`y = -(1)/(5)x - 1`

`x = -(1)/(5)y - 1`

`x + 1 = -(1)/(5)y`

`-5(x + 1) = -5(-(1)/(5)y)`

`-5(x) - 5(1) = y`

`-5x - 5 = y`

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

5.
`g(x) = (1)/(x - 1)`

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

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

`y(x) - y(1) = -1`

`xy - y = -1`

`xy = y - 1`

`(xy)/(y) = (y - 1)/(y)`

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

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

`f^(-1)(x) = 1 - (1)/(x)`

6.
`f(x) = -2x^(3) + 1`

`y = -2x^(3) + 1`

`x = -2y^(3) + 1`

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

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

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

`\sqrt[3]{-(1)/(2)x + (1)/(2)} = y`

`\sqrt[3]{-(1)/(2)x + (1)/(2)} = f^(-1)(x)`

7.
`g(x) = (-x - 5)/(3)`

`y = (-x - 5)/(3)`

`y(3) = 3((-x - 5)/(3))`

`3y = -x - 5`

`3x + 5 = -y`

`(3x + 5)/(-1) = (-y)/(-1)`

`-3x - 5 = y`

`-3x - 5 = f^(-1)(x)`