# 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 ->  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

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 Click here to see ALL problems on Rational-functions 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(13828)   (Show Source): You can put this solution on YOUR website!1) and . . . 2) . . . 3) . . . 1) Use x,y nomenclature Interchange x and y Solve for y. Answer by stanbon(57347)   (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.