Question

When comparing the f(x) = –x2 + 2x and g(x) = log(2x + 1), on which interval are both functions positive?

(–∞, 0)
(0, 2)
(2, ∞)
(∞, ∞)

Answer 1

I can help, give me a minute

Answer 2

omg thank youuuu

Answer 3

Here is a picture of both of your equations graphed on the same page
https://www.desmos.com/calculator/rzdujsvhya

Answer 4

got it

Answer 5

You can see that
f(x) = -x^2 + 2x
is positive between 0 and 2

Answer 6

You can also see that
g(x) = log (2x + 1)
is positive from 0 to infinity

Answer 7

so when do you think BOTH are positive?

Answer 8

like when they intersect

Answer 9

kind of... more like when are they both above the x axis?

Answer 10

yah thats what they intersect

Answer 11

above the x axis

Answer 12

(1.6,0.6)

Answer 13

nono we don't care about intersection

Answer 14

oh okay

Answer 15

sorry

Answer 16

f(x) = -x^2 + 2x
is positive between 0 and 2

g(x) = log (2x + 1)
is positive from 0 to infinity

so when are they equations both positive?

Answer 17

when they are above 0

Answer 18

correct

that is (0, 2) for f(x)
and (0, infinity) for g(x)

so when do the intervals (0, 2) and (0, infinity) overlap?

Answer 19

(1,1) ?

Answer 20

okay well that answers my question

Answer 21

Can we do one more

Answer 22

to see if I get it

Answer 23

ask separate questions on separate question posts

Answer 24

got it

Answer 25

to solve this without graphing, you could rewrite f(x) as 1-(x-1)², and if 1-(x-1)²>0 then (x-1)²<1 or -1<x-1<1 and 0<x<2.

you also have if g(x)>0 then 2x+1>10⁰=1 so 2x>0 and x>0