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We are given that $f(x)$ has domain $x \geq -4$ and $f(x) < -1$. All numbers in $\mathbb{R}$.

Now we want to find the domain of $3f(x+1)+4$. My solution is $x+1 \geq -4$ so new domain is $x \geq -5$ and $3f(x)+4 < -1$ so $f(x) < -\frac{5}{3}$.

Have I made any missteps here? Specifically, am I correct in treating the domain and range as having nothing to do with each other so their calculations are kept separate?

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  • $\begingroup$ What is $y$? I don't see it defined anywhere $\endgroup$
    – Andrei
    Commented Sep 26, 2022 at 15:24
  • $\begingroup$ @Andrei thanks for the catch. I changed it. $\endgroup$
    – Salazar_3854708
    Commented Sep 26, 2022 at 15:25

1 Answer 1

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The first part is correct. For the second part:$$f(x)<-1\\3f(x)<-3\\3f(x)+4<-3+4$$

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