# 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# .)