Question

I know that the answer to this is all real numbers less than or equal to 5. My question is how do you solve this (without a calculator)? Given f(x) = -3x^2 +5, what is the range of the function I tried to use -b/2a but I probably did it wrong. Thanks

Answer 1

find inverse function
y = f(x) = -3x^2 + 5
write x in terms if y
x = sqrt(-(y-5)/3)
inverse function is
f-1(x) = sqrt(-(x-5)/3)

domain of inverse is the range of the function

from inverse, inside sqrt must greater than or equal to 0 so that x-5 <= 0 which is x <= 5