Question

todos os valores de x, de modo que a expressão cos0=(3x+1)/5 exista, sao

Answer 1

$\displaystyle \text{A fun{\c c}{\~a}o cosseno est{\'a} limitada no intervalo de -1 a 1, ent{\~a}o:} \\\\ -1\leq\text {cos}(\theta) \leq 1 \\\\\\ -1\leq \frac{3\text x+1}{5} \leq 1 \\\\\\ \frac{3\text x+1}{5}\leq 1 \\\\\ 3\text x+1 \leq 5 \\\\ 3\text x\leq 4 \\\\ \boxed{\text x \leq \frac{4}{3}} \\\\ \text e \\\\\ \frac{3\text x+1}{5}\geq -1 \\\\\\ 3\text x+1 \geq -5 \\\\ 3\text x\geq -6 \\\\ \boxed{\text x \geq -2}\\\\ \underline{\text{Portanto}}:$

$\huge\boxed{\ -2\leq \text x \leq \frac{4}{3} \ }\checkmark \\\\\\ \text{ou} \\\\\\ \huge\boxed{\ [\ -2\ , \ \frac{4}{3}\ ]\ }\checkmark$