Quiz 2
Math 1050-002 (Summer 2002)
Tuesday , June 4 , 2002
Name:
1
Student ID:
? Show all your works for full/partial credit.
1. (5 pts) Find the equation of line passing through the points, (4, 3), (−4, −4)
7
ANSWER: Slope is 3−(−4)
4−(−4) = 7/8. Now we have an equatuin of y = 8 x + b. To
find b, put one point (4, 3) into the equation. That is, 3 = 78 (4) + b , so that
b = − 12 . The equation is y = 78 x − 12
2. (5 pts) If a function is given by
f (x) =
1
x+1
, then what are the values of f (0), f ( 12 ), and f (x3 ) ?
ANSWER: f (0) = 1, f ( 12 ) =
1
1/2+1
= 23 , f (x3 ) =
1
.
x3 +1
3. (5 pts)
Determine whether the given function is even, odd, or neither. Use the definition
of even and odd function to verify your conclusion.
f (x) = x4 + x2 + 3
ANSWER: f (−x) = (−x)4 + (−x)2 + 3 = x4 + x2 + 3 = f (x). It is an even
function by the definition.
4. (5 pts)
What is the inverse function of f (x) = 5x ? Verify that f (f −1 (x)) = x .
ANSWER: Its inverse function is 15 x. It is shown as f (f −1 (x)) = f ( 15 x) = 5 15 x =
x.