1001 Algebra Problems.PDF

725.Which of the following is the inverse function

for f(x) =  5 xx–+^12 ,x≠–^25 ?

a.f–1(y) =  52 yy–+^11 ,y≠–^15 

b.f–1(y) = ^25 yy+–1^1 ,y≠^15 

c.f–1(y) =– 52 yy–– 11 ,y≠^15 

d.f–1(y) = ^25 yy++1^1 ,y≠–^15 

726.Assume that the function fhas an inverse f-1,
and the point (1, 4) is on the graph ofy= f(x).
Which of the following statements is true?
a.If the range of f-1is [1,∞), then f(0) is not
defined.
b.f–1(4) = 1
c.The point (4, 1) must lie on the graph of
y= f–1(x).
d.All of the above statements are true.

727.Which of the following is the inverse of
f(x) = x3 + 2?
a.f–1(y) = ^3 y – 2
b. f–1(y) = ^3 y– 2
c.f–1(y) = ^3 2 – y
d.f–1(y) = ^32 – ^3 y

728.Which of the following are characteristics of
the graph off(x) = 2 – xx

2

+

1

^1?

I.The function is equivalent to the linear func-

tion g(x) = 2 – (x+ 1) with a hole at x= 1.

II.There is one vertical asymptote, no hori-

zontal asymptote, and an oblique asymptote.

III.There is one x-intercept and one y-intercept.

a.I only

b.II only

c.II and III only

d.I and III only

729.Which of the following are characteristics of

the graph off(x) = (2 –x(xx)

2

(x

2)

+ 2 3)?

I.The graph has a hole at x= 2.

II.y= 1 is a horizontal asymptote and x= 0

is a vertical asymptote.

III.There is one x-intercept and one y-intercept.

a.I and III only

b.I and II only

c.I only

d.none of these choices

730.Which of the following functions is decreasing

on (–∞,0)?

a.f(x) = x^3

b.f(x) = 2x+ 5

c.f(x) = ^1 x

d.f(x) = 3

731.Which of the following functions is increasing

on (0,∞)?

a.f(x)= x^3

b.f(x) = 2x+ 5

c.f(x) = |x|

d.all of the above

732.Which of the following statements is false?

a.The domain of any polynomial function is

the set of all real numbers.

b.There exists a rational function whose

domain is the set of all real numbers.

c.A rational function must have both a vertical

and a horizontal asymptote.

d.All of the statements are true.

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