MATH 1050 SECTION 2 QUIZ 5
FALL 2009
1. 5 points.
f (x) =
x+4
3x + 2
Find f −1 (x)
solution.
y=
x+4
.
3x + 2
x=
y+4
.
3y + 2
Exchange x and y:
Cancel the denominator:
3xy + 2x = y + 4.
Group the terms with y:
3xy − y = 4 − 2x.
Pull out y:
y(3x − 1) = 4 − 2x.
Solve for y:
y=
4 − 2x
.
3x − 1
2. 5 points. Does the function f (x) = (x − 4)2 + 8 have an inverse? Justify your answer.
solution. This function does not have an inverse because it does not pass the horizontal line test. 3. 5 points. Find the vertex of f (x) = 3x2 + 12x − 2.
solution. The x-coordinate of the vertex is given by the formula h = −
is k = f (h) = −14.
b
= −2. The y-coordinate
2a
4. 5 points. Write f (x) in standard form:
f (x) = a(x − h)2 + k.
solution. Note that a is 3, the leading coefficient of f . Plugging in h and k, we have
f (x) = 3(x + 2)2 − 14.
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