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)
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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) (Show Source): You can put this solution on YOUR website!
1)
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1)
Use x,y nomenclature
Interchange x and y
Solve for y.
Answer by stanbon(75887) (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.
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