Question #c5542

2 Answers
Jan 11, 2018

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)

Jan 11, 2018

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