Find (f+g)(x) , (f-g)(x) , (f/g)(x) and (g/f)(x) for the following f and g . State the domain for f(x)=(√2x+3) ; g(x)=x²-2?
1 Answer
Jul 4, 2015
See below.
Explanation:
State the domain for f(x)=(√2x+3) ; g(x)=x²-2.
For
Also for
Neither function involves the possibility of dividing by zeros or of trying to find an even root of a negative number. Nor of any other undefined expression.
# = (sqrt2 x+3) + (x^2-2)#
# = x^2+sqrt2 x +1#
# = (sqrt2 x+3) - (x^2-2)#
# = sqrt2 x +3 -x^2 +2#
# = -x^2+sqrt2 x + 5#
# = (sqrt2 x+3) / (x^2-2)# (For#x != +- sqrt2# .)
# = (x^2-2)/(sqrt2 x+3)# (For#x != - 3/sqrt2# .)