Some basic maths questions....

1. Find h(3) if h(t) = 2t^2-5 t < - 1 and 4 - 3t t >= -1
h(3)=4-3(3)=4-9=-5

2. Find a so that the 2 lines don't intersect: y = 4x + 2, y - 3 = ax
y = 4x + 2, y - 3 = ax

if a=4, then the second line is y=4x+3 which does not intersect with y = 4x + 2

3. Find g(f(-2)) if f(x) = log^4 (-8x) and g(x) = x - 3

f(-2)=log^4 (16)=2
g(f(-2))=2-3=-1

4. Rewrite 5^b = a in logarithmic form

5^b=a
blog5=loga

5. Rewrite as a single logarithm: 1/2 log x + 4 logy - 2 log z
1/2 log x + 4 logy - 2 log z
log (x)^(1/2)+log(y^4)-log(z^2)
=log(x^(1/2)y^4/z^2)

6. solve for y: log^3 y - log^3 (y-1) = 2
log^3 y - log^3 (y-1) = 2
log^3 [y / (y-1)] = 2
y/(y-1)=9
y=9y-9
y=9/8

7. If f(x) = - x^2 and g(x) = x +4, find the values of x so that g(f(x)) > 0
g(f(x)) > 0
-x^2+4>0
x^2-4<0
(x-2)(x+2)<0
-2<2

8. If tan(theta) = B where theta is an angle in quadrant I, express sin(theta) in term of B

sin(theta)=B/sqrt(B^2+1)

9. sin(thta + pi) = -sin(theta)

2008-04-24 23:45:50 補充：
&gt >
&lt

2008-04-24 23:45:58 補充：
&lt