Question

Find the following composite functions and state the domain of each.

Answer 1

We have the functions:

f(x) = x² and g(x) = x² + 7

So, we can compose them to obtain:

(a)

`\begin{gathered} (f\circ g)(x)=f(g(x))=f(x^2+7)=(x^2+7)^2=(x^2)^2+2\cdot7x^2+7^2 \\ \\ =x^4+14x^2+49 \end{gathered}`

Since there are no restrictions on the values of x, the domain of this composite function is:

`\mleft\lbrace x\in\mathfrak{\Re }\mright\rbrace`

In interval notation, this domain can be written as: (-∞, ∞).