+23 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.\(Find/ all/ complex/ numbers/ z/ such/ that/ z^2 = 2i. Write/ your/ solutions/ in/ a+bi form, separated/ by/ commas/. So/, "1+2i, 3-i" is/ an/ acceptable/ answer/ format/, but/ "2i+1; -i+3"/is not./ (Don't /include/ quotes/ in /your answer.) Note: /This /problem/ is/ not/ about /functions.\)
+73 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!
+129852 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
+23 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.\(Let/ f/ be /a /function/ such/ that/ f(x+y) = x + f(y) /for/ any/ two/ real/ numbers/ x/ and/ y/. If f(0) = 2, then/ what/ is/ f(2012)?\)
