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MA 161 Review โ Chapter 1 - Functions Name________________
1. True or False?
FALSE ln(๐ฅ 2 + 3๐ฅ + 2) = ln ๐ฅ 2 + ln 3๐ฅ + ln 2
TRUE ln(๐ฅ 2 + 3๐ฅ + 2) = ln(๐ฅ + 2) + ln(๐ฅ + 1)
TRUE 2 ๐ฅ^ = ๐ ๐ฅ ln 2
TRUE โ๐ฅ + 3 = (๐ฅ + 3)1/
FALSE
1 ๐ฅ 4
FALSE โ๐ฅ 2 + 1 = ๐ฅ + 1
TRUE โ๐ฅ 2 + 4๐ฅ + 4 = ๐ฅ + 2
FALSE
1 ๐ฅ 2 +
1 ๐ฅ 2
1 4
2. โSimplifyโ
b.
f.
5๐ โ1^ ๐ โ^
โ
3. Solve each equation.
(a)
๐ ๐ฅ^ = ๐ ๐ฅ^
(^2) โ
(b)
4(3 ๐ฅ^ ) = 20 โ ๐ฅ =
ln 5
ln 3
(d)
7 โ 2๐ ๐ฅ^ = 5 โ ๐ฅ = 0
(h)
(i)
4. Find ๐ฅ.
a.
log 2 32 = ๐ฅ โ ๐ฅ = 5
b.
log 2
c.
log 2 โ
3
d.
log 2 โ
3
MA 161 Review โ Chapter 1 - Functions Name________________
e.
log 2 ๐ฅ = โ3 โ ๐ฅ =
f.
log 2 ๐ฅ = 4 โ ๐ฅ = 16
g.
log 2 ๐ฅ =
h.
log 2 ๐ฅ = โ
3
5. Find f โ1^ (๐ฅ) โ or explain why it doesnโt exist.
(a)
๐ โ1^ (๐ฅ) =
(b)
๐ โ1^ (๐ฅ) = ๐ฆ =
- For the given function, find (and simplify) (i) f (x + h) (ii) f (x + h) f (x) (iii) f^ (x+h h) f^ (x)
(a) f (x) = 3x + 7
f (x + h) = 3(x + h) + 7 = 3x + 3h + 7
f (x + h) f (x) = (3x + 3h + 7) (3x + 7) = 3h f (x + h) f (x) h
3 h h
(b) f (x) = x 2
f (x + h) = (x + h) 2 = x 2 + 2xh + h 2 f (x + h) f (x) = (x 2 + 2xh + h 2 ) (x 2 ) = 2xh + h 2 f (x + h) f (x) h
2 xh + h 2 h
h(2x + h) h = 2x + h
(c) f (x) = (^) x^1 +
f (x + h) =
(x + h) + 3
x + h + 3
f (x + h) f (x) =
x + h + 3
x + 3
(x + 3) (x + h + 3)(x + 3)
(x + h + 3) (x + h + 3)(x + 3)
=
(x + 3) (x + h + 3) (x + h + 3)(x + 3)
h (x + h + 3)(x + 3)
f (x + h) f (x) h
h (x+h+3)(x+3) h
h (x+h+3)(x+3) h 1
h (x + h + 3)(x + 3)
h
=
(x + h + 3)(x + 3)
a few basic algebra reminders....
- Find an equation of the line that satisfies the given conditions: (a) passes through (-1,-1) and (3, 7) Answer: y = 2x + 1.
(b) passes through (7, 2) and (5, 2) Answer: y = 2.
(c) passes through (-1, 3) and (-1, 5) Answer: x = 1.
(d) passes through (-2, -6) and is parallel to y = 2x + 3. Answer: y = 2x 2.
(e) passes through (4, 2) and is perpendicular to y = 2x + 3. Answer: y = 12 x + 4.
- Simplify the expression below (no negative exponents, no compound fractions). (a) โ 3 y
y 2 4
y 3
y 2
y 2
y 4
y 7 (b) 5 x ^2 ( 2 y 0 ) 3 = 5
x 2
x 2
x 2 (c) 2 x+ 3 x 2
x + 2
x 2 3
2(x 2) 3(x + 2)
2 x 4 3 x + 6
(d) x+ p^3 x 2 + 16
x+ p^3 x 2 + 1
x + 4 3
p x 2 + 16
x + 4 3
p x 2 + 16
- Combine into a single logarithmic term. (a) ln(x + 2) ln(x 1) = ln
x + 2 x 1
(b)
ln(x + 2) ln(x 1) + ln(x + 1) = ln
x + 2 x 1
(x + 2)(x + 1) x 1
