SOLUTION
We want to find the domain of the composite function
[tex]\begin{gathered} f\circ g,\text{ where} \\ f(x)=4x+32 \\ g(x)=x+7 \end{gathered}[/tex]
Now
[tex]\begin{gathered} f\circ g\text{ } \\ means\text{ putting g\lparen x\rparen into f\lparen x\rparen, } \end{gathered}[/tex]
We have
[tex]\begin{gathered} f\circ g=4(x+7)+32 \\ =4x+28+32 \\ =4x+60 \end{gathered}[/tex]
Now the domain of 4x + 60 is all real numbers. Because any value of x, where positive or negative will give a real number that is a positive of negative number. So the domain is positive infinity to negative infinity.
Hence the answer is
[tex](-\infty,\infty)[/tex]
The first option is correct
