Question

Hello! I need some help with this homework question, please? The question is posted in the image below. I've completed section (a) of this question. Q10 - session b

Answer 1

Given:

`\begin{gathered} f(x)=\sqrt[]{x} \\ g(x)=4x+7 \end{gathered}`

To find:

`g\circ f`

And its domain, follow the steps below.

Step 01: Substitute x in g(x) by f(x).

`g\circ f=g(f(x))`

Then, given g(x), substitute x in this equation by f(x).

`\begin{gathered} g(x)=4x+7 \\ g(f(x))=4\cdot\sqrt[]{x}+7 \\ g(f(x))=4\sqrt[]{x}+7 \end{gathered}`

Thus,

`g\circ f=g(f(x))=4\sqrt[]{x}+7`

Step 02: Find the domain.

The domain is the set of all possible input values, that is, the set of all possible x-values.

Since there is no square root of negative roots, x can not be negative.

Then, the domain is x ≥ 0.

Domain:

`D=\mleft\lbrace x\mright|x\ge0\}`

Answer:

gof:

`g\circ f=4\sqrt[]{x}+7`

Domain:

`D=\lbrace x|x\ge0\}`