Question

Help please. i need it ASAP. 35 points

Answer 1

`\(h(g(f(x)))\)` simplifies to
`\(2\sqrt{(3x-1)/(3)} + 1\)`.

Let's go through the calculation:

1. Start with
`\( f(x) = (x-1)/(x) \)`:

`\[ g(f(x)) = g\left((x-1)/(x)\right) \]`

2. Now, substitute
`\( g(x) = √(x+2) \)` into the expression:

`\[ h(g(f(x))) = h\left(\sqrt{(x-1)/(x)+2}\right) \]`

3. Finally, substitute
`\( h(x) = 2x + 1 \)` into the expression:

`\[ h(g(f(x))) = 2\left(\sqrt{(x-1)/(x)+2}\right) + 1 \]`

The correct expression is
`\( h(g(f(x))) = 2\sqrt{(3x-1)/(3)} + 1 \)`.

To conclude, the composition
`\(h(g(f(x)))\)` involves three functions:
`\(f(x) = (x-1)/(x)\), \(g(x) = √(x+2)\)`, and
`\(h(x) = 2x+1\)`. Substituting
`\(f(x)\)` into
`\(g(x)\)`, and then the result into
`\(h(x)\)`, simplifies to
`\(2\sqrt{(3x-1)/(3)} + 1\)`, representing the combined transformation of the original functions.