Answer
See an explanation
Work Step by Step
$f(x)=\sqrt{x+1},$ $g(x)=\frac{2}{x}$
a.$(f+g)(x)=\sqrt{x+1}+\frac{2}{x}=\frac{x\sqrt{x+1}+2}{x}$
for all ${ x|x \geq -1 \cup x\ne 0}$
b.$(f-g)(x)=\sqrt{x+1}-\frac{2}{x}=\frac{x\sqrt{x+1}-2}{x}$
for all ${ x|x \geq -1 \cup x\ne 0}$
c. $(f \times g)(x)=\sqrt{x+1}\times \frac{2}{x}=\frac{2\sqrt{x+1}}{x}$
for all ${ x|x \geq -1 \cup x\ne 0}$
d. $(f/g)(x)=\frac{\sqrt{x+1}}{\frac{2}{x}}=\frac{x\sqrt{x+1}}{2}$
for all ${ x|x \geq -1 \cup x\ne 0}$
e. $(f+g)(3)=\frac{8}{3}$
f. $(f-g)(4)=\frac{4\sqrt{5}-2}{4}$
g. $(f\times g)(2)=\sqrt{3}$
h. $(f/g)(1)=\frac{\sqrt{2}}{2}$
