Question

Question #c5542

Answer 1

Domain: `x in RR`

Explanation:

Actually `f(x)=-2x^2+3` is defined for all complex numbers as well, so technically the domain is `x in CC`.

For the subquestions:
`f(color(blue)5)=-2 * color(blue)5^2+3=-50+3=-47`
and
`f(color(green)(-1))=-2 * (color(green)(-1))^2+3=-2+3=1`

Perhaps a more interesting question would have been "What is the range..."
Note that `f(x)` has a maximum value of `3` (when `x=0`)
and has no lower limit;
so the Range is `f(x) in [3,-oo)`

Answer 2

Domain = `RR` , `f(5)=-47` , `f(-1)=1`

Explanation:

`f(x)=-2x^2+3`

`f` is defined for any real value of `x` so the domain of `f` is the set of all real numbers so, `RR`
You can tell that by looking at the graph (as `y` approaches any number on the range, `x` can get any value from `-oo` to `+oo`)
graph{-2x^2+3 [-10, 10, -5, 5]}

For `f(5)` plug in `f` the value `x_1=5`
For `f(-1)` plug in `f` the value `x_1=-1`

• `f(5)=-2*5^2+3=-2*25+3=-50+3=-47`
• `f(-1)=-2*(-1)^2+3=-2*1+3=-2+3=1`