Linear and Quadratic Equations
3(2x−1)=4x+5
x=4
(3x2+2x)+(x2−5x)
4x2−3x
What is the definition of a function?
each input has exactly one output
Solve and state restrictions: (x+2)/(x-1) = 3
x=5/2, x≠1
sin(5π/3)
-√3/2
(x−3)2=7
x=3±√7
(3x+5)(2x−2)
6x2+4x-10
Is x=y2 a function?
nope
Solve √(x+5) = x-1
x=4 (check for extraneous)
Simplify sinx/cscx + cosx/secx
sin2x + cos2x = 1
x2+kx+9=0
k=±6
According to the Factor Theorem, what does it mean if f(2)=0f(2) = 0f(2)=0?
(x−2) is a factor of the polynomial
Find the inverse of f(x)= 2x+1
f-1(x)= 1/2x - 1/2
(4x+2)/5 = ((3-x)/6) + 2
x=3
Solve on [0, 2π): sin(2x) = √3/2
x = π/6, π/3, 7π/6, 4π/3
A quadratic equation has no real solutions and a leading coefficient of 1. What must be true about its discriminant, and why?
The discriminant is negative; the parabola does not intersect the x-axis
Simplify (2+3i)(1−i)
5+i
How would you determine if a function has an inverse?
If it is one-to-one; each output corresponds to exactly one input
ln(x) = ln(6-x)
x=3
Simplify sinx(1+cosx) / 1-cos2x
cscx + cotx
2x2−3x=5x−6
x=2 and x=−2/3
Divide 4+2i/1-i
1+3i
If f(g(x))=x, what relationship do f and g have?
They are inverse functions
Solve logx + log(2x+5) - log7 = 0
x=1
If secθ=-5 and sinθ>0, find cscθ
(5√6)/12