Thread: Functions

1) Simplify function
g(g−1(2x−3))

2)
State the intervals on which the following function is negative: function

f(x)= (1-x)^3(1+x)
x^6(-1-2x)

Express your answers using interval notation. For an interval (ab) , simply write (a,b). For in interval (−b) or (a)

The first is a definition check.

By Definition, the answer is '2x-3'. There are no calculations required. You tell me why.

Hi

Originally Posted by lemontea

1) Simplify function
g(g−1(2x−3))

What's the matter with this question ?

2)
State the intervals on which the following function is negative: function

f(x)= (1-x)^3(1+x)
x^6(-1-2x)

You should first study the sign of , of , of and of then you'll be able to conclude using the rules concerning the quotient and the product of real numbers.

i still dont get the second question ><''

Originally Posted by lemontea

i still dont get the second question ><''

If you were asked to find where is negative, you could do this :

and

Hence

• if then and hence
• if then and hence
• if then and hence

We can conclude that .

Is it clearer ?

i got the answers (-inf,-1) and (-1/2,1)...but it's incorrect..does anyone know why?

Originally Posted by lemontea

i got the answers (-inf,-1) and (-1/2,1)...but it's incorrect..does anyone know why?

Who says that they are incorrect? Those are the intervals that I find.