<p>Here is the question my jolly colleagues:
if r(x)= 6x+5 and s(r(x))= 2x-1, then s(x)= ?</p>
<p>Usually I am the master of functions, but the explanation on the book had me puzzled. Can someone tell me how to solve this, either algebraically or by other methods?</p>
<p>By the way, the answer is (x-8)/3.</p>
<p>Thank you all.</p>
<p>You pretend that you know s(x) is going to be linear (for simplicity). (This is the long way to do it.)</p>
<p>So...</p>
<p>s(x)=ax+b</p>
<p>x=r(x) for now.</p>
<p>a(6x+5)+b=2x-1</p>
<p>You can easily see that you need to divide by 3, or multiply by 1/3 to create the 2x.</p>
<p>1/3(6x+5)+b=2x-1</p>
<p>2x+5/3+b=2x-1</p>
<p>5/3+b=-1</p>
<p>b=-8/3</p>
<p>Common denominator it...</p>
<p>(x-8)/3</p>
<p>Of course, on the test you can do MUCH faster by just scanning the answer choices.</p>
<p>just is. </p>
<p>Try to use math to get 2x-1 to equal 6x+5.</p>
<p>is there a way to do it by plugging in?</p>
<p>Dude. Just plug in the answer choices for S(X)
Lets pick ur choice that
S(X) = (x-8)/3 ok?
Now plug in for X , 6x + 5
now do ((6x+5)-8)/3
there is ur plugging in way.</p>
<p>Hey "dude", as blatant as it may seem to you, I got confused in the middle of your explanation--I could not see what your were trying to illustrate due to post's strange punctuation and lack of detail. If it is not too much trouble, could you please list the steps taken? I realize this may seem like a fatuous question on my part, but I rarely have trouble with functions and really feel like I should grasp this.</p>
<p>Input from anyone is welcome.</p>
<p>Well.. you said your the master of functions. this is one of the more simpler ones because all you have to do it plug in answer choices... i still don't get why you don't get it.
1. backsolve (pick the answer (x-8)/3)
2. plug in R(X) because you're looking for S(R(X)) which is the same thing as S(6x + 5). Plug in 6x + 5 for the X in the equation (x-8)/3.</p>
<p>Oh, we were looking for the answer choice that yields 2x-1...Great gyro321, thanks for helping me. This is definitely a quicker route.</p>
<p>Ok. I'm doing this w/o looking at any of the previous posts:</p>
<p>r(x)= 6x+5 and s(r(x))= 2x-1, then s(x)= ?</p>
<ol>
<li><p>That's the easy part.
s(6x+5)= 2x-1</p></li>
<li><p>We need something to somehow reduce the 6x to a 2x. Why not use a fraction (1/3) as a slope? Why 1/3? When you multiple 6x by 1/3 you get 2/3.</p></li>
</ol>
<p>s(x) = (1/3)x</p>
<ol>
<li><p>Let's try that.
(1/3)(6x+5) = 2x+5/3</p></li>
<li><p>Not quite what we wanted, but the slope came out good. Let's modify the equation. The b is off by 8/3. Let's fix that.
s(x) = (1/3)x - 8/3</p></li>
<li><p>Let's try again:
(1/3)(6x+5) - (8/3)
2x+(5/3)-(8/3)
2x+3/3
2x-1</p></li>
<li><p>Since you got the answer...s(x) = (1/3)x - 8/3</p></li>
</ol>
<p>That's how I got it....and I'm still hoping for something close to an 800. (700 in april...anyway...that doesn't quite matter)</p>
<p>I think the best way of doing this problem on the SAT is by plugging in numbers. </p>
<p>Given:
r(x) = 6x + 5
s(r(x)) = 2x - 1</p>
<p>Therefore,
s(6x + 5) = 2x - 1</p>
<p>Plug in values for x get values for s(6x + 5)</p>
<p>x=0; 6x + 5 = 5; s(6x +5) = -1
x=1; 6x + 5 = 11; s(6x +5) = 1
x=2; 6x + 5 = 17; s(6x +5) = 3</p>
<p>Now use those as points on a line</p>
<p>(5, -1) (11, 1) (17, 3)</p>
<p>The slope is 1/3 and the "y"-intercept is -8/3</p>
<p>s(x) = (1/3)x - (8/3) or (x-8)/3</p>
<p>I got an 800 on the SAT M section when I took it the first time, so I probably know something about doing well, hehe. Just kidding. ^^</p>
<p>let s(x)=ax+b,</p>
<p>S(r(x))=a(6x+5)+b
->2x-1=6.a.x+5.a+b
->2(x)-1=6.a.(x) +(5a+b)
equating,
2=6.a -> a=1/3
and,
-1=5a+b
->-1=(5/3)+b
->b=-8/3</p>
<p>Therefore, S(x)=ax+b=(x/3)+(-8/3)=(x-8)/3</p>
<p>
[quote]
if r(x)= 6x+5 and s(r(x))= 2x-1, then s(x)= ?
[/quote]
This is a question for the SAT Subject Math.</p>
<p>s(6x+5) = 2x-1 (Eq.1)</p>
<p>Let t = 6x+5, then
x = (t-5)/6</p>
<p>Plug it in Eq.1
s(t) = (2)[(t-5)/6] - 1
s(t) = (t-8)/3.</p>
<p>We can consider t an independent variable and replace it with any other letter
s(x) = (x-8)/3.</p>
<p>its quite easy
from the equation ,u could assum that s(x) could written in form Ax+B(<em>)
then s(r(x))=A(r(x))+B
for r(x)=6x+5
A(r(x))+B=A(6x+5)+B
so 2x-1=6Ax+(5A+B)
then 2=6A
-1=5A+B
U could easily work out,A=1/3
B=-3/8
PLUG THEN INTO (</em>)
THERE U GO!</p>
<p>LOL yeah i agree, just plug in the answer choices. Quicker than trying to actually solve it.</p>
<p>Here is the question my jolly colleagues:
if r(x)= 6x+5 and s(r(x))= 2x-1, then s(x)= ?</p>
<p>This isn't too bad.</p>
<p>We know that s(x) must be a linear function which is of the form mx+b where m is the slope of the function and b is the y-intercept.</p>
<p>Now substitute r(x) for x in s(x) = mx+b</p>
<p>m(6x+5) + b = 2x-1
(6m)x + 5m + b = 2x-1</p>
<p>The only x coefficient on the left side of this equation is 6m, and the only x coefficient on the right side is 2, so we can set these equal.</p>
<p>6m = 2, m = 1/3</p>
<p>Now we can solve for b.</p>
<p>5m + b = -1
5(1/3) + b = -1
5/3 + b = -3/3
b = -8/3</p>
<p>So the function s(x) is defined as:</p>
<p>s(x) = (1/3)x -8/3</p>