1. ## Polynomial

Real quick question

Given that f(x) = 5x^2 - 12

i) what is the degree of this polnomial ? ( Is this 2?)

iii) with the aid of a flow chart, or otherwise , write down the expression for f^-1(x).

What does the f^-1 mean?

cheers for all the help guys.

2. Originally Posted by mxmadman_44
Real quick question

Given that f(x) = 5x^2 - 12

i) what is the degree of this polnomial ? ( Is this 2?)
The degree of a polynomial is the largest sum of the exponents of the terms. In this case, there is only one variable, so its simple: the largest exponent is 2, so this is a polynomial of degree 2, or a quadratic.

Originally Posted by mxmadman_44
iii) with the aid of a flow chart, or otherwise , write down the expression for f^-1(x).

What does the f^-1 mean?

cheers for all the help guys.
What happened to question ii)?
The notation $\displaystyle f^{-1}(x)$ indicates the inverse function. The inverse function has the property that, if $\displaystyle y = f(x)$ then $\displaystyle f^{-1}(y) = x$.

There's an algebraic method of finding these.

Let
$\displaystyle y = f(x) = 5x^2 - 12$

Now exchange the roles of x and y:
$\displaystyle x = 5y^2 - 12$

Now solve for y:
$\displaystyle 5y^2 = x + 12$

$\displaystyle y^2 = \frac{x + 12}{5}$

$\displaystyle y = \sqrt{\frac{x + 12}{5}}$

Now we have that $\displaystyle f^{-1}(x) = y = \sqrt{\frac{x + 12}{5}}$.

(Note: We really need to be a bit more careful than I was about domains and ranges. If you need more accuracy here, just let me know.)

-Dan

3. i is good. The degree is 2

$\displaystyle f^{-1}(x)$ indicates the Inverse Function, the lovely function that gives you back whatever f(x) did to the value in the fisrt place.

For example:

$\displaystyle f(x) = 2x$

$\displaystyle f^{-1}(x) = x/2$

$\displaystyle f(6) = 12$ and $\displaystyle f^{-1}(12) = 6$

See how we got back what we started with?

The usual methodology is "Swap and Solve"

If $\displaystyle y = 5x^{2} - 12$, then REsolve for 'y' in $\displaystyle x = 5y^{2} - 12$. This will give you an Inverse RELATION. The result that it is or is not a function is an additional important consideration that will cause you problems on this one. Solve that last expression for "y" and see if you can tell why it's a problem.

4. ## thanks

thanks guys i understand it now. It all came rushing back to me. My notes were not so clear but i completely understand it now

thankyou