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# Function multiplication, equation of a circle & tangent line

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(1) The table gives the values of the functions f and g. Use the table to evaluate the expressions below. If there is not enough information given, state the information you would need to evaluate the expression.

x 0 1 2 3 4 5

3 5 0 2 1 4

2 7 1 5 3 0

a.] g(f(3))
b.] f(g(5) )
c.] f(g(1) )

(2) Given (x)=(4+?x)^9, find functions f, g, and h such that r(x)=(f?g?h)(x).

(3) Solve and show your work.
a.] 2.6(1.04)^t=4.1
b.] 4(1.171)^x=7(1.088)^x
c.] log_2 3+log_2 x=log_2 5+log_2 (x-2)

(4) Consider the circle x^2+y^2-6x-8y=0.
Find the point of intersection of the two tangent lines to the circle which pass through the points (0,0) and (6,0), respectively.

##### Solution Summary

This solution explains four separate problems on functions, function multiplication, equation of a circle and finding its tangent line through a point, and other mathematical expressions.

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Please see the attached file for the complete solution.
* Note the two graphs are included in the last question *

(1) The table gives the values of the functions f and g. Use the table to evaluate the expressions below. If there is not enough information given, state the information you would need to evaluate the expression.
a.]
f(3) = 2
g(2) = 1
g(f(3)) = 1

b.]
g(5) = 0
f(0) = 3
f(g(5)) = 3

c.]
g(1) = 7
f(7) is not given, so this information is needed ...

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