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:

Answer 1

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, ∞)