1. ## Functions

The function f is defined f:x = 1- 6x -3x^2
1. evaluate ff(-2)

2. Calculate the exact values of x which map onto themselves under the function f.

ok i could do the first one(reletively simple) BUT the 2nd one i dont understand the question and cant do. CAN anyone explain what is meant by the 2nd question?????

Also this to
3. Determine the range of f
4. Explain why f has and inverse.

Question 2 ,3 and 4 i basically just dont understand can anyone explain them???

2. ## Re: Functions

The function f is defined f:x > 1- 6x -3x^2
sorry, but I'm not familiar with the function notation you are using.

From what you've posted, I see the inequality ...

$x > 1 - 6x - 3x^2$

... is that what you meant?

3. ## Re: Functions

sorry
F:x = 1- 6x -3x^2

4. ## Re: Functions

Hi KingMAths,

This is what I think you mean

$f(x) = 1- 6x - 3x^2$
1. Was to find $f(f(-2))$ (for which you have an answer already)

2. Was to find all x such that $f(x) = x$
so we have
$x = 1- 6x - 3x^2 \implies 1 - 7x -3x^2 = 0 \implies x = \frac{-7 \pm \sqrt{61}}{-6}$ by solving the quadratic.

3. The range of $f(x)$ thats simple enough if you write $f(x) = 4 -3(x+1)^2$ so the range is $[4,-\infty)$ as $x \in R$

Now the 4 question should be easy for you to solve.

Kalyan