What is the domain and range of f(x) = sqrt(4-3x) + 2f(x)=43x+2?

1 Answer
Apr 15, 2015

Domain x: inR, 3x<=4
Range y: inR, y>=2

The domain would be all real numbers such that 4-3x>=0 Or such that 3x <=4, that is x<= 4/343. This is because the quantity under the radical sign cannot be any negative number.

For the range, solve the expression for x.
y-2= sqrt(4-3x)43x Or,
4-3x= (y-2)^2(y2)2, Or
y-2= sqrt(4-3x)43x
Since 4-3x has to be >=0, y-2 >=0,y20
Hence Range would be y ;in R, y>=2