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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 realvalued functions fx 2x10 and gx x1 find the composition fg and specify its domain using interval notation fgxDomain of fg class=

Respuesta :

we have

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

g(x)=x-1

therefore

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

simplify

[tex](f•g)(x)=\sqrt[]{2x+8}[/tex]

Remember that the radicand cannot be a negative number

so

[tex]\begin{gathered} 2x+8\ge0 \\ 2x\ge-8 \\ x\ge-4 \end{gathered}[/tex]

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

the domain is the interval [-4, ∞)