Question 125139
1.  Given some function f(x), to find f(a) just replace x with a in the function and do the arithmetic.


2.  The domain of a function is the set of values for which the function is defined.  For the function {{{F(x)=x+4/x}}}, F is defined everywhere except where the denominator in the fractional term becomes zero, in other words, 
{x | x is a real number, {{{x<>0}}}}, or in interval notation:  ({{{-infinity}}},{{{0}}}) U ({{{0}}},{{{infinity}}})


3. {{{x=4y + 3}}};
{{{2x + 5y = 6}}}


You have an expression for x in the first equation, so substitute it for x in the second equation.


{{{2(4y+3) + 5y = 6}}}


Now solve for y:
{{{8y+6 + 5y = 6}}}
{{{8y+5y = 6-6}}}
{{{13y = 0}}}
{{{y=0}}}


Substitute this value for y into the first equation:

{{{x=4(0) + 3}}}
{{{x=3}}}


Your solution set is (3,0)


4. You aren't given a method to use, but this one can be done by Gaussian Elimination.


{{{2x - y =5}}} and {{{x + 2y = 10}}}


Multiply the first equation by 2
{{{4x-2y=10}}}


Add the second equation to the first:
{{{5x+0y=15}}}


Solve for x:
{{{5x=15}}}
{{{x=3}}}


Substitute this value for x into either equation:
{{{2(3)-y=5}}}


Solve for y
{{{6-y=5}}}
{{{-y=5-6}}}
{{{y=1}}}


Your solution set is (3,1)

You can do the other two problems the same way.