Question

On #10 i need help to solve this. please and thank you.

Answer 1

10a.
`f(x) = x - 4`

`h(x) = √(x - 5)`

`(f - h)(6) = (6 - 4) - (√(6 - 5))`

`(f - h)(6) = 2 - √(1)`

`(f - h)(6) = 2 - 1`

`(f - h)(6) = 1`

10b.
`f(x) = x - 4`

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

`(f * g)(x) = (x - 4)((1)/(x - 3))`

`(f * g)(x) = (x - 4)/(x - 3)`
Domain: (-∞, 3) ∨ (3, ∞) x
Interval Notation: (3 < x < 3), (3 > x > 3)

10c.
`g(x) = (1)/(x - 3)`

`h(x) = √(x - 5)`

`(g * h)(x) = ((1)/(x - 3))(√(x - 5))`

`(g * h)(x) = (√(x - 5))/(x - 3)`

10d.
`f(x) = x - 4`

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

`h(x) = \sqrt[3]{x - 7}`

`h(x) = (f * g)(x)`

`\sqrt[3]{x - 7} = (x - 4)((1)/(x - 3))`

`\sqrt[3]{x - 7} = (x - 4)/(x - 3)`

`(\sqrt[3]{x - 7})^(3) = ((x - 4)/(x - 3))^(3)`

`x - 7 = ((x - 4)^(3))/((x - 3)^(3))`

`(x - 3)^(3)(x - 7) = (x - 4)^(3)`

`(x^(3) - 9x^2 + 27x + 27)(x - 7) = (x^(3) - 12x^(2) + 48x - 64)`

`x^(4) - 16x^(3) + 90x^(2) - 216x + 189 = x^(3) - 12x^(2) + 48x - 64`

`x^(4) + 90x^(2) - 216x + 189 = 17x^(3) - 12x^(2) + 48x - 64`

`x^(4) + 102x^(2) - 216x + 189 = 17x^(3) + 48x - 64`

`x^(4) + 102x^(2) + 189 = 17x^(3) + 264x - 64`

`x^(4) + 102x^(2) + 253 = 17x^(3) + 264x`

`x^(4) - 17x^(3) + 102x^(2) - 264x + 253 = 0`

`x = 4\ or\ 8`