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

1 Answer
bp
Apr 15, 2015

Domain x: in∈R, 3x<=≤4
Range y: in∈R, 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)√4−3x Or,
4-3x= (y-2)^2(y−2)2, Or
y-2= sqrt(4-3x)√4−3x
Since 4-3x has to be >=0, y-2 >=≥0,y−2≥0
Hence Range would be y ;in∈ R, y>=≥2

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