The solution set of the equation `e^(4x) - 5e^(2x) + 4 = 0` over `R` is
A. `{1, 4}`
B. `{– 4, – 1})`
C. `{– 2, – 1, 1, 2})`
D. `{– log_e(2), 0, log_e(2)}`
E. `{0, log_e(2)}`
Algebra, MET2 2009 VCAA 5 MC
Let `f: R -> R,\ f (x) = x^2`
Which one of the following is not true?
- `f(xy) = f (x) f (y)`
- `f(x) - f(-x) = 0`
- `f (2x) = 4 f (x)`
- `f (x - y) = f(x) - f(y)`
- `f (x + y) + f (x - y) = 2 (f (x) + f(y))`
Functions, MET1 2013 VCAA 9
The graph of `f(x) = (x - 1)^2 - 2, x in [– 2, 2]`, is shown below. The graph intersects the `x`-axis where `x = a.`
Find the value of `a.` (1 mark)
Note: other parts of this question are out of the syllabus and not included.
Graphs, MET2 2015 VCAA 7 MC
The range of the function `f:\ text{(−1, 2]} -> R,\ \ f(x) = -x^2 + 2x-3` is
- `R`
- `text{(−6, −3]}`
- `text{(−6, −2]}`
- `text{[−6, −3]}`
- `text{[−6, −2]}`
Show Worked Solution
`text(A sketch of the equation:)`
| `y` | `=-x^2 + 2x-3` |
| `dy/dx` | `=-2x+2` |
`=>\ text(Concave down with turning point when)\ \ x=1,`
`:. text(Range) = (-6,-2]`
`=> C`
Graphs, MET2 2012 VCAA 3 MC
The range of the function `f: text{[−2, 3)} -> R,\ f(x) = x^2 - 2x - 8` is
A. `R`
B. `text{(−9, −5]}`
C. `text{(−5, 0)}`
D. `text{[−9, 0]}`
E. `text{[−9, −5)}`
Show Worked Solution
`text(Sketching the quadratic:)`
`:.\ text(Range) = [−9,0]`
`=> D`