Question

For the real-valued functions f(x) = 2x+10 and g(x) = x-1, find the composition f•g and specify its domain using interval notation.(f•g)(x)=Domain of f•g: (The 2x+10 is square rooted)

Answer 1

Okay, here we have this:

We need to meke the composition (f•g)(x), so in the function f we will replace x with the function g:

$\begin{gathered} \mleft(f•g\mright)\mleft(x\mright)=\sqrt[]{2(x-1)+10} \\ =\sqrt[]{2x-2+10} \\ =\sqrt[]{2x+8} \end{gathered}$

Now let's find the domain of (f•g)(x):

2X+8≥0

2X≥-8

X≥-4

Finally we obtain the following domain: [-4,∞)