Function Graphs
\[\large (X-1)(X-3)(X-5)(X-7)\ldots (X-97) < 0 \]
How many positive integers \(X\) satisfy the inequality above?
by
Mahtab Hossain
Determine whether the function \(f(x) = \ln(x+ \sqrt{1+x^2} )\) is an odd function or an even function.
by
Akhil Bansal
\[\left| 1-\left| 1-\left| x-1 \right| \right| \right| =\alpha \]
Find the value of \(\alpha\) for which this equation has exactly 4 distinct solutions. If the value of \(\alpha\) is \(A\), then find \(2A\).
by
Aditya Tiwari
Find the area of the region bound by the equation \[|x+2y|+|2x-y|=10\]
by
Daniel Liu
Given the graph \( y = \ln x \), which of these statements describes the transformations to get the graph of \( y = \ln (4x^2 + 4x + 1) \) for \( x > - \frac{1}{2} \)?
\(\quad \text{(1)}\) Translate to the left by 1 and up by \( \ln 4 \), then scale vertically by 2.
\(\quad \text{(2)}\) Translate to the left by \(\frac{1}{2}\) and up by \( \ln 2 \), then scale vertically by 2.
\(\quad \text{(3)}\) Translate to the left by 1 and up by \( \ln 2 \), then scale vertically by 2.
\(\quad \text{(4)}\) Translate to the left by \( \frac{1}{2} \) and up by \( \ln 4 \), then scale vertically by 2.
by
Chung Kevin