## anonymous one year ago Solve the equation the square root of the quantity x minus 6 plus 2 equals 6 for the variable. Show each step of your solution process.

1. anonymous

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2. Nnesha

first combine like terms -6_2 and then take square both sides to cancel out square root

3. Nnesha

you can write square root as 1/2 root $\huge\rm \sqrt{x} = x^\frac{ 1 }{ 2 }$ when you take square $\huge\rm \sqrt{x} = (x^\frac{ 1 }{ 2 })^2$ both 2 cancel each othr out and then you x is left that's how you can take square to cancel ot square root :-)

4. Owlcoffee

$\sqrt{x-6+2}=6$ The first step is alwas... ALWAYS trying to remove the square root since it is quite bothersome to deal with in algebra level. So, we will square both sides: $(\sqrt{x-6+2})^2=6^2$ That'll cancel the square root and give us the following: $x-6+2=6^2$ $x-6+2=36$ And that is much simpler to solve, is it not?

5. anonymous

thank you both!! can you help me with one more??

6. anonymous

Let f(x) = 4x2 + x + 1 and g(x) = x2 – 2. Find g(f(x)). Show each step of your work.

7. Owlcoffee

That is what we call a "composite function", what you do is replace the function on all the x's of the other function, so if you have: $f:f(x)=4x^2+x-1$ $g:g(x)=x^2-2$ Then, in order for the transformation to occurr: $g(x),f(x) \rightarrow (g,f): g(f(x))$ We will have an equivalent of this: $(g,f):g(f(x))=(f(x))^2-2$ So, therefore, g(f(x)) will be composed of: $g(f(x))=(4x^2+x+1)^2-2$

8. anonymous

then what..?

9. Owlcoffee

That's it.

10. anonymous

oh ok cool lol