Answer:
[tex]x \in [1, 6)[/tex]
Step-by-step explanation:
Because the function is decreasing:
[tex]g(x_1) > g(x_2) \iff x_1 < x_2[/tex]
So:
[tex]g(x^2) > g(5x + 6) \iff x^2 < 5x + 6\\x^2 < 5x + 6\\x^2 - 5x - 6 < 0\\x^2 - 5x + 6.25 - 12.25 < 0\\x^2 - 2\cdot 2.5x + 2.5^2 < 12.25\\(x - 2.5)^2 < 12.25\\x - 2.5 \in (-3.5; 3.5)\\x \in (-1; 6)\\[/tex]
Combining that with the domain [tex]D_g = [1; \infty )[/tex]
[tex]x \in [1, 6)[/tex]
