Answer by insipidintegrator for A silly question on range of a quadratic...
I think the OP’s doubt is that “f(x)$\geq\frac 14$“ states that any values taken by f(x) are greater than or equal to $\frac 14$, but not that f(x) takes all values greater than or equal to $\frac...
View ArticleAnswer by Martin R for A silly question on range of a quadratic function.
Your calculation is correct and complete if you write it like this:$$\begin{align}&\text{$y$ is in the range of $f$} \\\iff &x^2 + 3x + 2-y=0 \text{ for some } x \in \Bbb R \\\iff...
View ArticleAnswer by ultralegend5385 for A silly question on range of a quadratic function.
In your solution, you show that $x$ has a real value if $y\geq -1/4$ using discriminant of a quadratic. Well this works the other way too! If $y\geq -1/4$, then the quadratic has nonnegative...
View ArticleAnswer by Macavity for A silly question on range of a quadratic function.
I would write this as $y = (x+\frac32)^2-\frac14$, from which it is obvious what the range would be, as the square term takes all nonnegative values.
View ArticleA silly question on range of a quadratic function.
Let $f:\mathbb{R}\to\mathbb{R}\space|\space f(x) = x^2 + 3x + 2 \space\forall\space x \in\mathbb{R}$We are asked to find the range of the function $f$I begin as follows:Assume $y=x^2 + 3x + 2$ for some...
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