SOLUTION: I need help with this setting up this question and I'm not sure what the format of the answer should be: Let f(x)=sqrt(x+2) -x. Find all numbers x, if any, such that f(x)= -4

Algebra ->  Functions -> SOLUTION: I need help with this setting up this question and I'm not sure what the format of the answer should be: Let f(x)=sqrt(x+2) -x. Find all numbers x, if any, such that f(x)= -4      Log On


   

Question 1047495: I need help with this setting up this question and I'm not sure what the format of the answer should be:
Let f(x)=sqrt(x+2) -x. Find all numbers x, if any, such that f(x)= -4
Found 2 solutions by Boreal, MathLover1:
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt(x+2)-x=-4
sqrt(x+2)=x-4
square both sides
x+2=x^2-8x+16
x^2-9x+14=0
(x-7)(x-2)=0
x=7,2
Check for extraneous roots.
sqrt (9)-(7)=-4. 3-7=-4, so x=7 is a solution.
Try 2
sqrt(-2+2)-(2)=-4
0-2 does not equal 4.
f(7)=-4
graph%28300%2C300%2C-10%2C10%2C-10%2C10%2Csqrt%28x%2B2%29-x%2B4%29 This is a graph of sqrt(x+2)-x+4. Where it equals 0 is a root of this function.

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

f%28x%29=sqrt%28x%2B2%29+-x
Find all numbers x, if any, such that f%28x%29=+-4
-4=sqrt%28x%2B2%29-x
x-4=sqrt%28x%2B2%29-x%2Bx
x-4=sqrt%28x%2B2%29.........square both sides
%28x-4%29%5E2=%28sqrt%28x%2B2%29%29%5E2
x%5E2-8x%2B16=x%2B2
x%5E2-8x%2B16-x-2=0
x%5E2-9x%2B14=0
x%5E2-2x-7x%2B14=0
%28x%5E2-2x%29-%287x-14%29=0
x%28x-2%29-7%28x-2%29=0
%28x-7%29+%28x-2%29+=+0
solutions:
if %28x-7%29++=+0->x=7
if %28x-2%29++=+0->x=2
check:
-4=sqrt%28x%2B2%29-x if x=7
-4=sqrt%287%2B2%29-7
-4=sqrt%289%29-7 .......since sqrt%289%29= 3 or -3, we can use 3 only
-4=3-7

-4=-4

-4=sqrt%28x%2B2%29-x if x=2
-4=sqrt%282%2B2%29-2
-4=sqrt%284%29-2 .......since sqrt%284%29= 2 or -2, we can use -2 only
-4=-2-2

-4=-4