- Sketch the graphs of the functions `f(x)=x-1` and `g(x)=(1-x)(3+x)` showing the `x`-intercepts. (2 marks)
- Hence, or otherwise, solve the inequality `x-1<(1-x)(3+x)`. (2 marks)
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a.
b. `-4<x<1`
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a. `g(x)\ text{cuts}\ xtext{-axis at 1 and}\ -3.`
`g(x)_max=g(-1)=4`
`text{Find intersection of graphs:}`
| `(1-x)(3+x)` | `=x-1` | |
| `3+x-3x-x^2` | `x-1` | |
| `x^2+3x-4` | `=0` | |
| `(x+4)(x-1)` | `=0` |
`text{Intersections at:}\ (1,0), (-4,-5)`
b. `text{From the graph:}`
`x-1<(1-x)(3+x)\ \ text{when}\ \ -4<x<1`
`text{Test}\ \ x=0:`
`0-1<(1-0)(3+0)\ \ =>\ \ -1<3\ \ text{(correct)}`