Question

For which value(s) of x is f(x)>0

Answer 1

Answer:

Let's say that

f

(

x

)

=

x

2

−

10

The graph below shows

y

=

f

(

x

)

:

graph{x^2-10 [-6, 6, -15, 15]}

When we want

f

(

x

)

>

0

, we want

y

>

0

, or all the values of

x

where

f

(

x

)

>

0

.

In this instance,

x

2

−

10

>

0

x

2

>

10

x

>

√

10

x

<

−

√

10

Proof:

x=10:

10

2

−

10

=

100

−

10

=

90

x=6

6

2

−

10

=

36

−

10

=

26

x=1:

1

2

−

10

=

1

−

10

=

−

9

x=-1:

(

−

1

)

2

−

10

=

1

−

10

=

−

9

x=-6

(

−

6

)

2

−

10

=

36

−

10

=

26

x=-10:

(

−

10

)

2

−

10

=

100

−

10

=

90