Let fx square root x1 and gx xx 1 Find the functions f g

Let f(x) = square root x+1 and g(x) = x/x + 1. Find the functions f - g, fg and f/g.

Solution

f(x) = sqrtx +1 g(x) = x/(x+1)

Find

Subtract the two functions: (f-g)(x) = f(x) - g(X) = sqrtx +1 - x/(x+ 1)

= (x+1)sqrtx +x+1 -x)/(x+1)

=( (x+1)sqrtx +1)/(x+1)

Multiply both functions to get (f.g)(x) = (sqrtx +1)x/(x+1) = (xsqrtx +x)/(x+1)

Divide both functions to get (f/g) (x) = (sqrtx +1) / x/(x+1)

= (x+1(sqrtx +1)/x