Math questions pre algebra?

Question

My Math teacher gave us some math problems and told us to google it so see what other people came up with.... here goes....

Find the Domain
1. g(x)= 1/3x-3

2. f(x)= (the square root sign) -x-2

Solve...
1. x^3=x

2. x^2=-5x=24

Simplify
1. x^2+2x-3/x-5

2. x^3-27/x-3

3. (2x^-5y^-1)-3/(-5x^-3y^-4)-2

4. (x^-2y^3/-2x^-5y^7)^-3

Answer 1

2)  f(x) = the square root sign -x  - 2

f(x) =sqrt(-1(x + 2))

Substitute i^2 = -1 in the f(x)

f(x) = sqrt(i^2 ( x + 2)

f(x) = isqrt (x + 2)

We can find the Domain sqrt(x + 2) = 0

Take square each side

x + 2 = 0

Subtract 2 from  each side

x + 2 - 2 = 0 - 2

x + 0 = - 2

x = - 2

The domain is x = - 2

 

Answer 2

f(x) =sqrt(-1(x + 2))

Substitute i^2 = -1 in the f(x)

f(x) = sqrt(i^2 ( x + 2)

f(x) = isqrt (x + 2)

We can find the Domain sqrt(x + 2) = 0

Take square each side

x + 2 = 0

Subtract 2 from  each side

x + 2 - 2 = 0 - 2

x + 0 = - 2

x = - 2

The domain is x = - 2

Answer 3

Find the domain

1) The linear function

Make the table of values to find ordered pairs that satisfy the equation.

Choose values for x and find the corresponding values for y.

x		(x, y )
-2
0
2
-4
6

Draw a coordinate plane.

Plot the coordinate points.

Then sketch the graph, connecting the points with a line.

Since x can be any real number, there is an infinite number of ordered pairs that can be graphed. All of them lie on the line shown.

Notice that every real number is the x - coordinate of some point on the line.

Also, every real number is the y - coordinate of some point on the line.

So, the domain and range are both all real numbers, and the relation is continuous.

Domain of is all real numbers.

Answer 4

Find the domain

2) The radical function

Step - 1 Determine the index of the radical.

In this case the index is 2.

Index is  even.

Step - 2 Since the index is even , set the expression inside the radical greater than or equal to zero.

Step - 3 solve the inequality.

Add 2 to each side.

Multiply each side of inequality by negitive one and flip the symbol.

Domain of is .

Answer 5

Solve

2) The equation x² - 5x = 24

Subtract 24 from each side.

x² - 5x - 24 = 0

Solve the equation by using factrization.

Multiply first term x² and last term - 24 = -24x²

The correct pair of the terms -8x and 3x multiply to -24x² and add to -5x.

Replace the middle term -5x with -8x + 3x.

 x² - 8x + 3x - 24 = 0

Group the terms into two pairs.

(x² - 8x) + (3x - 24) = 0

Factor out x from the first group  and factor out 3 from the second group.

 x(x - 8) + 3(x - 8) = 0

Factor out common term x - 8.

(x + 3)(x - 8) = 0

Apply Zero Product Property :  For any real numbers a and b, if ab = 0, then either a = 0, b = 0, or both a and b equal zero.

x + 3 = 0 and x - 8 = 0

x = -3 and x = 8

Solutions are x = -3 , 8.

Answer 6

Simplify

1) The rational expression

• Now factorise the numrator of the above fraction.

x² + 2x  - 3

Multiply first term x² and last term -3 = -3x²

The correct pair of the terms 3x and -x multiply to -3x² and add to 2x.

Replace the middle term 2x with 3x - x.

= x² + 3x - x - 3

Group the terms into two pairs.

= (x² + 3x) + (- x - 3)

Factor out x from the first group  and factor out 1 from the second group.

= x(x + 3) - 1(x + 3)

Factor out common term x + 3.

= (x + 3)(x - 1)

x² + 2x  - 3 = (x + 3)(x - 1)

Subsstitute the numarator value in the fraction.

.

Answer 7

Simplify

4)

Apply exponent property

Apply exponent property

Apply exponent property

Answer 8

Find the domain

1)The rational function

We know that all possible values of x  is domain of a function.

A rational function is simply fraction and in a fraction the denominator cannot be equal to 0 because it would be undefined.

To find which number make the fraction undefined create an equation where the denominator is not equal to zero.

So the domain of the function all real numbers except .

Domain of is .