SOLUTION: Given: f(x)=x^2-4 g(x)=sqrt 2x+4 1)f(x)=o when x= 2)f(g(x)) 3)g(f(0)) 4)find the inverse of f(x)

Algebra ->  Rational-functions -> SOLUTION: Given: f(x)=x^2-4 g(x)=sqrt 2x+4 1)f(x)=o when x= 2)f(g(x)) 3)g(f(0)) 4)find the inverse of f(x)      Log On


   

Question 155916: Given: f(x)=x^2-4 g(x)=sqrt 2x+4
1)f(x)=o when x=
2)f(g(x))
3)g(f(0))
4)find the inverse of f(x)
Found 2 solutions by Fombitz, stanbon:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
1)f%28x%29=x%5E2-4=0
x%5E2=4
x=2 and x=-2
.
.
.
2)f%28x%29=x%5E2-4
g%28x%29=sqrt%282x%2B4%29
f%28g%28x%29%29=%28sqrt%282x%2B4%29%29%5E2-4
f%28g%28x%29%29=%282x%2B4%29-4
f%28g%28x%29%29=2x
.
.
.
3)f%28x%29=x%5E2-4
g%28x%29=sqrt%282x%2B4%29
g%28f%28x%29%29=sqrt%282%28x%5E2-4%29%2B4%29
g%28f%28x%29%29=sqrt%282x%5E2-8%2B4%29
g%28f%28x%29%29=sqrt%282x%5E2-4%29
g%28f%280%29%29=sqrt%282%280%29%5E2-4%29
g%28f%280%29%29=sqrt%28-4%29
g%28f%280%29%29=2%2Asqrt%28-1%29
g%28f%280%29%29=2i
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.
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1)f%28x%29=x%5E2-4
y=x%5E2-4 Use x,y nomenclature
x=y%5E2-4 Interchange x and y
y%5E2=x%2B4 Solve for y.
y=0%2B-sqrt%28x%2B4%29
f%5E%28-1%29%28x%29=0%2B-sqrt%28x%2B4%29

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Given: f(x)=x^2-4 g(x)=sqrt 2x+4
1)f(x)=o when x=
--
x^2-4 = 0
(x-2)(x+2) = 0
x = 2 or x = -2
--------------------------
2)f(g(x))
f[g(x)] = f[sqrt(2x+4)]
= (sqrt(2x+4))^2 -4
= 2x+4 - 4
= 2x
----------------------------
Given: f(x)=x^2-4 g(x)=sqrt (2x+4)
3)g(f(0))
g(f(0)) = g(-4) = sqrt[(-4)^2+4] = sqrt[20] = 2sqrt(5)
------------------------------
4)find the inverse of f(x)
Interchange x and y to get:
x = y^2-4
solve for y:
y^2 = x+4
y = +/-sqrt(x+4)
========================
Cheers,
Stan H.