Question

F(x) = √4x
g(x) = 3x + 5
Find (x). Include any restrictions on the domain.

Answer 1

The composition f(g(x)) is given by
`\(√(12x + 20)\)`, with the restriction that
`\(x \geq -(5)/(3)\)` to ensure the expression inside the square root is non-negative, thereby defining the domain.

Assuming you want to find the composition f(g(x)), where
`\(f(x) = √(4x)\)` and g(x) = 3x + 5, you can proceed as follows:

`\[ f(g(x)) = √(4(3x + 5)) \]`

Now, simplify the expression inside the square root:

`\[ f(g(x)) = √(12x + 20) \]`

To find any restrictions on the domain, note that the expression inside the square root (12x + 20) must be non-negative for the function to be defined. Therefore, solve the inequality:

`\[ 12x + 20 \geq 0 \]`

`\[ 12x \geq -20 \]`

`\[ x \geq -(5)/(3) \]`

So, the composition
`\(f(g(x)) = √(12x + 20)\)` is defined for
`\(x \geq -(5)/(3)\).`