Relations and Functions

Let f(x)= e x and g(x)= x4-2x3+3x2-2x+22x2-2x+1. Then the domain of f g is

1. (0, )
2. [1, )
3. R
4. [0, )

Answer

(3) R

Solution

f g= g(x) needs g(x)>0.

Numerator = (x2-x+1 )2+1 1>0

Denominator =2 (x- 12 )2+ 12>0

g(x)>0 for every real x domain = R

Answer: (3)