Algebra

Algebra
Question 1)
F(x) = -x2-4x +3For x= -2 then the f(x) = -(-2)2-4(-2)+3=7Question 2)
3(x-2)=-4(x+8)+103x-6= -4x-32+107x=-16X=-167Question 3)
F(x) = xx-4All values would be real except when the value of x=4 hence the domain is
D: allR: x≠4Question 4
Slope (m) = -3/7, y-intercept(c) =-4Y=mx+cHence, y=-37x -4Question 5
Slope(m) = -2, passes through (-1,6) hence the y intercept is
Taking a point (x,y) where the line passes then
Gradient is ∆y/∆x = y-6x-(-1)=-2y-6x+1=-2Hence y=-2x+4Question 6
(2x-7)(x+4)=02x(x+4)-7(x+4)=02x(x+4)=7(x+4)2×2+8x=7x+28 hence 2×2+x-28=0Using the factor method the values of X=7/2 , -4Question 7
Vertex f(x) =3×2-6x+8f(x) = a(x – h)2 + k, where (h, k) is the vertex hence f(x) =3(x-1)2+5the vertex =(1,5)Question 8
Y intercept of f(x) =(x-2)(x+1)(x-3)=(x^2-x-2)(X-3)=x^3-〖5x〗^2+x+6For a cubic curve, the y-intercept must always be at x=0 hence y=6Y(0)=6Question 9
f(x)=2×2-x+7 ; g(x)=x-1(f-g)(x)= 2x^2-x+7-(x-1)= 2x^2-2x+8Question 10
f(x)=x^2+3; g(x)=x+4; (f o g )(-2)g(-2)=2hence f(g(x))=2^2+3 =7
Question 11
F(x)=2x-4, f^-1 (x)Y=2x-4; y-4=2xX= (y-4)/2f^-1 (x)= (x-4)/2Question 12
A=p(1+r/n)^ntP=1000, r=6%, T=5yrs, n=4A=1000(1+(.06/4))^(5*4) = $1346.86Question 13
y∝x; y=∝1/√w hence y=kx/√wQuestion 14
Answer log3y=x
Question 15
Log2x=y
In the exponential form is 2y=xQuestion 16
5x/6- x/3=1/6; lcm =6Multiplying through by 6 we get 5x-2x=1Hence x=1/3Question 17
Log390=x
Logb x = Loga x/Loga b
Hence log 90/log 3
Question 18
If |x+2|=5 then squaring we get x+2=5 hence x=3 orx+2=-5 hence x=-7 Question 19
2X+3Y=10
4X-6Y=28
Multiply the first equation by 2 we get 4x+6y=20
Subtracting the two we get
8x=48 hence, x=6, Using in equation 2 then y=-2/3(6, -2/3)
Question 20
Multiply (3+2i)(3-2i)=5+0i