# Thread: Find a for f(x+6)=2x+a where f(a)=20

1. ## Find a for f(x+6)=2x+a where f(a)=20

I haven't a clue about how to do this. Its my last question and I've been looking at it for almost a half hour now with no result. Any help appreciated...thanks!

2. Originally Posted by GeeDee
I haven't a clue about how to do this. Its my last question and I've been looking at it for almost a half hour now with no result. Any help appreciated...thanks!
I think it's

f(x+6)=2x+a

f(x+6)=2(x+6)+20

0=2x+12+20

x=-16

(-16+6)=2(-16)+a

a=22

I just taking a guess here

3. Thanks....I just actually tried doing that before I read your post. But apparently the answer in the book tells me a=8/3 ?

4. Originally Posted by GeeDee
I haven't a clue about how to do this. Its my last question and I've been looking at it for almost a half hour now with no result. Any help appreciated...thanks!
If your book told you the answer is a = 8/3, then the book is wrong.

You have
$f(x + 6) = 2x + a$
and you want
$f(a) = 20$.

Well, if $f(x + 6) = 2x + a$ then

Let $y = x + 6 \implies x = y - 6$ so
$f(y) = 2(y - 6) + a$

$f(y) = 2y - 12 + a$

We want $f(a) = 20$, so
$f(a) = 2a - 12 + a = 20$

$3a - 12 = 20$

$3a = 32$

$a = \frac{32}{3}$

-Dan

5. Originally Posted by topsquark
If your book told you the answer is a = 8/3, then the book is wrong.

You have
$f(x + 6) = 2x + a$
and you want
$f(a) = 20$.

Well, if $f(x + 6) = 2x + a$ then

Let $y = x + 6 \implies x = y - 6$ so
$f(y) = 2(y - 6) + a$

$f(y) = 2y - 12 + a$

We want $f(a) = 20$, so
$f(a) = 2a - 12 + a = 20$

$3a - 12 = 20$

$3a = 32$

$a = \frac{32}{3}$

-Dan
i thought as much. i saw no need to introduce a new variable though.

$f(x + 6) = 2x + a = 2x + 12 - 12 + a = 2(x + 6) - 12 + a$

and then, continue as you did

6. Originally Posted by Jhevon
i thought as much. i saw no need to introduce a new variable though.

$f(x + 6) = 2x + a = 2x + 12 - 12 + a = 2(x + 6) - 12 + a$

and then, continue as you did
I was trying not to confuse the original poster with the "x + 6 - 6" thing. Maybe good, maybe not.

-Dan

7. Originally Posted by topsquark
I was trying not to confuse the original poster with the "x + 6 - 6" thing. Maybe good, maybe not.

-Dan
yeah, you're right. that maneuver does confuse some people