Question 48600: Please can someone help me solve the following. I would really appreciate some help.
1)How many imaginary zeros does the funtion f(x) = 3x4 + 2x3 + 4x + 7 have?
a. 0
b. 2 or 0
c. 4 or 2
d. 4, 2, or 0
2)Identify the real zeros for the function f(x) = x3 - 3x2 - 53x - 9.
3)Identify the real zeros to the nearest tenth for the function f(x) = x3 - 6x - 9.
a. 3.0
b. -.6, 1.4
c. .8, 2.0
d. -1.2, .4, 3.0
4)
Identify all zeros for the function f(x) = x3 - 6x2 + 10x - 8.
a. 1, 2, 4
b. 2, 2, 4
c. 4, 1 + i,1 - i
d. 4, 2 + i, 2 - i
5)If f(x) = x2 and g(x) = x + 2, find f[g(x)]
a. x2 + 2
b. x2 + 4x + 4
c. x2 + x + 2
d. x2 - x + 2
6)If f(x) = x3 + 4 and g(x) = x + 3, find [g • f](2)
a. 15
b. 12
c. 5
d. 129
7)Find the inverse of the function f(x) = 4x + 1.
a. f -1 (x) = x - 1/4
b. f -1 (x) = 1/4x - 1
c. f -1 (x) = 4x - 1
d. f -1 (x) = 1/4x - 1/4
8)Which of the following pairs of functions are inverse functions?
a. f(x) = 3x - 9, g(x) = -3x + 9
b. f(x) = 4 - x, g(x) = 4 + x
c. f(x) = x + 5, g(x) = x - 5
d. f(x) = x, g(x) = -x
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! 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.
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