Domain question (1 Viewer)
- Thread starter BlueGas
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keepLooking
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No solutions exist for x^2-2x+9=0 so I am guessing it is all real x?
BlueGas
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Yeah it's D.
How did that make you come to that conclusion that it was all real x?
keepLooking
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I thought a,b,c could all be correct be D was the most correct. Now that you actually asked, my logic is ..
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TQuadded
Breaking the limits.
You can't log a negative value. But since no whole number that is doubled (-2x) can be bigger than the number being squared (x^2), then it must always be positive. If you put any number 0 <= x <= 1, there's a plus nine at the end anyway, so x can be all real.
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so because the parabola is positive definite, any x-value you put will be more than zero. Yeh?)$ is defined for all values of $x\in \mathbb{R}$ such that $f(x)$ is strictly positive (because you can take the log of any positive number, but can't take logs of 0 or negative values). Since in this case, the quadratic inside the log is positive for all real $x$ (as shown by keepLooking), the logarithm is defined for all real $x$, so the domain is the set of all real $x$.$)
Yeah.