Question 71849: The degree three polynomial f(x) with real coefficients and leading coefficient 1, has -3 and +4i among its roots. Express f(x) as a product of linear and quadratic polynomials with real coefficients.
AND
for the function f(x) shown in the earlier problem, find the domain and range of f^-1(x)
Answer by venugopalramana(3286)   (Show Source):
You can put this solution on YOUR website! The degree three polynomial f(x) with real coefficients and leading coefficient 1, has -3 and +4i among its roots.
Express f(x) as a product of linear and quadratic polynomials with real coefficients.
ROOTS ARE -3,4I
SINCE COEFFICIENTS ARE REAL , CONJUGATE OF 4I ...THAT IS -4I MUST BE ROOT
HENCE F(X)
=[X+3][X-4I][X+4I]=[X+3][X^2-16I^2]=[X+3][X^2+16]
=X^3+3X^2+16X+48
for the function f(x) shown in the earlier problem, find the domain and range of f^-1(x)
FOR F(X) DOMAIN IS ANY REAL VALUE OF X and range is also any real
value of x.
HENCE FOR F^-1(X), ALSO THE DOMAIN AND RANGE ARE ALL REAL NUMBERS.
HOWEVER , PLEASE NOTE THAT f^(-x) is not a function as it does not give raise to a
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