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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)

For The Realvalued Functions Fx 2x10 And Gx X1 Find The Composition Fg And Specify Its Domain Using Interval NotationfgxDomain Of Fg The 2x10 Is Square Rooted class=

Answer :

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:

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

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

2X+8≥0

2X≥-8

X≥-4

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

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