Thread: Inverse problem

The inverse of a function is always useful to return a variable back to its original form.
a) Write x^2+6x+4 in the form (x+a)^2+b
b) Hence find the inverse of the function f(x)=x^2+6x+4
c) Explain why x >-5for this inverse function. (THAT IS MEAN'T TO BE X IS GREATER AND EQUAL TO MINUS 5)


CAN ANYONE HELP??

This is an exercise in "completing the square" for a quadratic equation. It's a handy trick that is useful for problems like this. Given the equation x^2 + bx + c, you can take the b coefficient, divide it by 2, square the result and then add and subtract the final result, like this:

f(x) = x^2 + bx + x = x^2 + bx + (b/2)^2 - (b/2)^2 + c = (x+(b/2))^2 -(b/2)^2 + c

So for your problem you have f(x)= x^2 + 6x + 4 = x^2 + 6x + 3^2 - 3^2 + 4 = (x+3)^2 -5.

That's part (a) done. Now rearrange to get it in the form x = .... You will end up with an equation that has a square root, which limits the range for f(x). And by the way, though in part (c) you wrote x >= -5 I think what you mean is f(x) >= -5.

a) try to complete the square. that is add and subtract the square of (6/2) that is 9 to get (x^2+6x+9-9+4) try now to write it as you like