Review question

# When is one of these functions greater than the other? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Ref: R6008

## Question

Functions $f$ and $g$ are defined by \begin{align*} f&:x\mapsto x(x-1), \\ g&:x\mapsto (x-1)(3x-5), \end{align*}

where $x\in \mathbb{R}$ in each case.

1. Find the solution set, $S$, of the inequality $f(x)\ge g(x)$.

2. Sketch the graph of $y=f(x)-g(x)$ for $x\in S$, and state the greatest and least values of $f(x)-g(x)$ for $x\in S$.