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
Jim H
Jul 4, 2015

See below.

Explanation:

State the domain for f(x)=(√2x+3) ; g(x)=x²-2.

For #f(x) = sqrt2 x+3#, the domain is all real numbers. #(-oo, oo)#

Also for #g(x) = x^2 -2#, the domain is all real numbers. #(-oo, oo)#.

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.

#(f+g)(x) = f(x)+g(x)#

# = (sqrt2 x+3) + (x^2-2)#
# = x^2+sqrt2 x +1#

#(f-g)(x) = f(x)-g(x)#

# = (sqrt2 x+3) - (x^2-2)#
# = sqrt2 x +3 -x^2 +2#
# = -x^2+sqrt2 x + 5#

#(f/g)(x) = f(x)/g(x)#

# = (sqrt2 x+3) / (x^2-2)# (For #x != +- sqrt2#.)

#(g/f)(x) = g(x)/f(x)#

# = (x^2-2)/(sqrt2 x+3)# (For #x != - 3/sqrt2#.)

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