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# Algebra b

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1.$$Let A(t) = 3- 2t^2 + 4^t. Find A(2) - A(1).$$

2.$$The function f satisfies f (\sqrt{x + 1}) = \frac{1}{x} for all x \ge -1,x\neq 0. Find f(2).$$

3.$$Let f(x) = \frac{3x - 7}{x + 1}. (Find) (the) (domain) (of) (f). (Give) (your) (answer) (as) an (interval).$$

4.$$Let f(x) = \frac{3x - 7}{x + 1}.(Find) the (range) of (f). (Give) (your) (answer) (as) (an) interval.$$

5.$$Let f(x) = \dfrac{2-3x}{5-2x}. For) what) value) of) (a) is ((f(a) = 3?)$$

6.$$Let f(x) = 3x^2 - 4x. Find( the( constant( k( such( that) f(x) = f(k - x) (for( all( real( numbers (x).$$

7.$$Let) (f) be )a) function) such) that) f(x+y) = x + f(y) for) any) two) real) numbers) (x) and) (y). If f(0) = 2, then) what) is)(( f(2012)?$$

8.

$$Let f(x) = x^2 + 4x - 31. For( what( value( of( a( is( there( exactly( one( real( value( of (x) such( that f(x) = a?$$

9.$$Find/ all/ complex/ numbers/ z/ such/ that/ z^2 = 2i. Write/ your/ solutions/ in/ a+bi form, separated/ by/ commas/. So/, "1+2i, 3-i" is/ an/ acceptable/ answer/ format/, but/ "2i+1; -i+3"/is not./ (Don't /include/ quotes/ in /your answer.) Note: /This /problem/ is/ not/ about /functions.$$

Apr 12, 2018

### 4+0 Answers

#1
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Hey, CPhill can you go back to the problem about the advertising? I kinda did a mistake in the problem. I put the exponent of 3 instead of 2. Can you give me the right answer? Sorry!

Apr 12, 2018
#2
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Here's a few :

1.

A(2)  - A(1)  =

[ 3  - 2(2)^2 + 4^2 ]  - [ 3 - 2(1)^2 + 4^1]

[ 3 - 8 + 16]  -  [ 3 - 2 + 4]

[ 11 ]  - [ 5]

6

3.     [ 3x - 7]  / [ x + 1]

We can put any x into the function  except  x  =  -1

So....the domain is  (-infinity , -1) U (-1, infinity )

4. [ 3x - 7 ] / [ x + 1 ]

Since we have a same power polynomial/ same power polynomial  we will have a horizontal asymptote   at    [ 3x ] / x   =    3

So....the range  is   (-infinity , 3) U (3 , infinity )

5.

3  =  [ 2 - 3a ]  /  [ 5 - 2a ]     multiply both sides by 5 - 2x

3 [ 5 - 2a]  = 2 - 3a

15 - 6a  = 2 - 3a      add 6a to both sides, subtract 2 from each side

13 = 3a  divide both sides by

13/3  =   a   Apr 12, 2018
#3
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Thanks a ton!!!

plzhelp  Apr 12, 2018
#4
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1.$$The/ function /f/ satisfies/ f(\sqrt{x + 1}) = \frac{1}{x} /for/ all/x \ge -1, x\neq 0. Find f(2).$$

2.$$Let/ f(x) = 3x^2 - 4x. Find/ the/ constant/ k/ such/ that/ f(x) = f(k - x) for/ all/ real /numbers/ x.$$

3.$$Find/ all/ complex /numbers/ z/ such /that/ z^2 = 2i. Write /your /solutions/ in/ a+bi /form/, separated/ by/ commas./ So,/ "1+2i, 3-i" /is/ an/ acceptable/ answer/ format,/ but/ "2i+1; -i+3"/ is/ not./ (Don't/ include/ quotes/ in/ your/ answer.)/ Note: /This/ problem /is /not /about/ functions.$$

4.$$Let/ f/ be /a /function/ such/ that/ f(x+y) = x + f(y) /for/ any/ two/ real/ numbers/ x/ and/ y/. If f(0) = 2, then/ what/ is/ f(2012)?$$

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Apr 12, 2018