# Function multiplication, equation of a circle & tangent line

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Please see the attached file for the complete solution.

(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.

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##### 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.

(please see the attached file)

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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