Question

Please HELP!
f(x)= 2x+3 for x less than equal to 0
g(x)= x^2-6x for x less than equal to 3

Find the set of values of x which satisfy gf(x) is less than equal to 16.

Answer 1

I got x less than equal to -/+ 2.5. But the answer says the range is -2.5<x<0. How so?

Answer 2

I don't know , give me your work, and we check together, is it ok to you?

Answer 3

Okay. Sure.

Answer 4

So, I did it like this.
gf(x)= (2x+3)^2-6(2x+3)
=4x^2-9

Answer 5

Then I put
\[4x^2-9\le16\]

Answer 6

yeap

Answer 7

\[x \le2.5\]

Answer 8

So after putting on the number line, the range I got was

Answer 9

+- 2.5

Answer 10

\[-2.5\le x \le 2.5\]

Answer 11

I know what the mistake is. you have to add the condition of f (x) which is x<0

Answer 12

Why not consider g(x) x <3 ? That would allow x=2.5?

Answer 13

because if x <0 , of course x<3 , right?

Answer 14

satisfy that condition already

Answer 15

you have 3 conditions:
x<0
x<3 and
-2.5< x < 2.5
combine them you have to take the answer that -2.5<x<0

Answer 16

because for that combination, you satisfy 2 conditions above.

Answer 17

got what i mean?

Answer 18

Okay. Thank you so much! :)

Answer 19

yw