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 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.)