Answer
See an explanation
Work Step by Step
$f(x)=2x^2+3,$ $g(x)=4x^3+1$
a.$(f+g)(x)=2x^2+3+4x^3+1=4x^3+2x^2+4$
for all ${x|x \in\mathbb{R}}$
b.$(f-g)(x)=2x^2+3-4x^3-1=-4x^3+2x^2+2$
for all ${x|x \in\mathbb{R}}$
c. $(f \times g)(x)=(2x^2+3)(4x^3+1)=8x^5+2x^2+12x^3+3=8x^5+12x^3+2x^2+3$
for all ${x|x \in\mathbb{R}}$
d. $(f/g)(x)=\frac{2x^2+3}{4x^3+1}$
for all ${x|x \in\mathbb{R} \ne \sqrt[3] {-\frac{1}{4}}}$
e. $(f+g)(3)=4(27)+2(9)+4=130$
f. $(f-g)(4)=-4(64)+2(16)+2=-222$
g. $(f\times g)(2)=8(32)+12(8)+2(4)+3=363$
h. $(f/g)(1)=5/5=1$
