Question 48600
1)How many imaginary zeros does the function f(x) = 3x^4 + 2x^3 + 4x + 7 have?
f(x) has no changes of sign so has no real zeros.
Therefore f(x) has 4 complex roots. They could be two complex with 
multiplicity two, so.
c. 4 or 2
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2)Identify the real zeros for the function f(x) = x^3 - 3x^2 - 53x - 9.
 Graphing you find a zero, x=9.
 Using synthetic division the remaining factor is x^2+6x+1
 Using the quadratic formula you find:
x=[-6+-sqrt(36-4(1)(1))]/2=[-3+-4sqrt(2)]/2 = (-3/2)+-2sqrt2
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3)Identify the real zeros to the nearest tenth for the function 
f(x) = x^3 - 6x - 9.
Graphing you find a zero, x=3
Graphing you get one zero at x=3.
Other factor is x^2+3x+3
x=[-3+-sqrt(9-12)]/2
x=[-3+-isqrt3]/2
a. 3.0
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4)Identify all zeros for the function f(x) = x^3 - 6x^2 + 10x - 8.
Graphing you find x=4 is a zero.
The remaining factor is x^2-2x+2
Zeros of that are x=[2+-sqrt(4-8)]/2= 1+-i
c. 4, 1 + i,1 - i
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5)If f(x) = x^2 and g(x) = x + 2, find f[g(x)]
f(g(x))=f(x+2) = (x+2)^2 = x^2+4x+4
b. x^2 + 4x + 4
6)If f(x) = x^3 + 4 and g(x) = x + 3, find [g o f](2)
g(f(2))= g(12)=15
a. 15
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7)Find the inverse of the function f(x) = 4x + 1.
Write y=4x+1
Interchange x and y to get x=4y+1
Solve for y: y=(x-1)/4 =(1/4)x-(1/4) 
d. f -1 (x) = 1/4x - 1/4 
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8)Which of the following pairs of functions are inverse functions?
f(g(x))=f(x-5)=x
g(f(x))=g(x+5)=x
Therefore the following are inverse to one another.
c. f(x) = x + 5, g(x) = x - 5
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Cheers,
Stan H.