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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:

For the real-valued functions f(x) = 2x+10 and g(x) = x-1, find the composition f-example-1
User Bethan
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1 Answer

10 votes
10 votes

we have


f(x)=\sqrt[]{2x+10}

g(x)=x-1

therefore


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

simplify


(f•g)(x)=\sqrt[]{2x+8}

Remember that the radicand cannot be a negative number

so


\begin{gathered} 2x+8\ge0 \\ 2x\ge-8 \\ x\ge-4 \end{gathered}

the domain is all real numbers greater than or equal to -4

the domain is the interval [-4, ∞)

User Jichi
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