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