SOLUTION: 1. Given f(x) = 4-x-x^2. Find f(3) 2. Find the domain of the function F given by F(x)=x+4/x 3. Solve by substitution: x=4y + 3; 2x + 5y = 6 4. Solve the system of equ

Question 125139This question is from textbook Intro to College Mathematics
: 1. Given f(x) = 4-x-x^2. Find f(3)
2. Find the domain of the function F given by F(x)=x+4/x
3. Solve by substitution: x=4y + 3; 2x + 5y = 6
4. Solve the system of equations: 2x - y =5 and x + 2y = 10. Put the answer in the form of (x,y).
5. Solve the system of equations: y=x+7; 2x +3y = 6. Put the answer in the form of (x,y).
6. Solve the system of equations: 4x - 3y =15; 3x + 5y =4. Put the answer in the form of (x,y).
This question is from textbook Intro to College Mathematics

Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
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 is defined everywhere except where the denominator in the fractional term becomes zero, in other words,
{x | x is a real number, }, or in interval notation: (,) U (,)

3. ;

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

Now solve for y:

Substitute this value for y into the first equation:

Your solution set is (3,0)

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

and

Multiply the first equation by 2

Add the second equation to the first:

Solve for x:

Substitute this value for x into either equation:

Solve for y

Your solution set is (3,1)
You can do the other two problems the same way.
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