f(x)=x^2;
g(x)=x-2
#composition of f and g
h(x)=g(f(x))#composition of f and g
i(x)=f(g(x)) #composition of g and f
print('gof(x)=', h(x))
print('fog(x)=',i(x))

# composition of functions practice f=s g=t
s(x)= x^2-5*x
t(x)= 7*x-2
l(x)=t(s(x))
m(x)=s(t(x))
print('sot(x)=', l(x))
print('tos(x)=',m(x))

# compining polynomials
#adding polynomials
print('the sum of s(x) and t(x)=',s(x)+t(x))
#subtracting polynomials
print('the difference of s(x) and t(x)=',s(x)-t(x))
#multiplying polynomials
print('the product of f(x) and g(x)=',f(x)*g(x))
#write expand to make the system simplify the equation
print('the product of f(x) and g(x) simplified=',expand(f(x)*g(x)))
#dividing polynomials
print('the quotient of f(x) and g(x)=',f(x)/g(x))

#factoring polynomials
n(x)= x^2+7*x-3
print(factor(n(x)))
w(x)=x^2-8*x+15
print(factor(w(x)))

#greatest common denominator
print('greatest common denominator is',gcd(s(x),t(x)))

#declare theta as a variable
theta=var('theta')
#solve equations
solve(x^2-5*x+6==0,x)
#I means imaginary
solve(x^2+x+1==0,x)
solve(2*sin(theta)==-1,theta)
solve(9+x^2+6*x+1==0,x)
solve(arccos(theta)==0,theta)
solve(4*x^3+8*x^2-3*x==0,x)