Algebra 2 domain and range and function operation?

Question

i dont understand this at all can someone give me step by step explanations?

1.)h(x)= 1/x+1

2.)g(x)= √x

3.) f(x)= -x^2

and multiplying.

4.) m(x)= 2x-1 and n(x)= x^2+2

and subtracting.

5.) f(x)= 3x^2-5x+1 and g(x)= 4x^2+9x-2

i have tried but i just dont understand. help!!!

Answer 1

1.)h(x)= 1/(x+1)

To find the domain you need to think of all possible x values that give y values.  You know that you can't divide by zero.  So you need to find what values of x make the bottom of the fraction zero.  I assume that x + 1 is the denominator of the fraction.  Set this equal to zero and solve for x.

x + 1 = 0

x = -1.

So x = -1 is not in the domain.  Every other number is, so the domain of h(x) is (-∞, -1) U (-1, ∞)

As for the range you want to know what values of y are possible given the values of x in the domain.  When x is positive then the fraction is positive and when x is negative then the fraction is negative.  So h(x) can be any number except zero because the fraction will never be zero.  Then the range is (-∞, 0) U (0, ∞).

2.)g(x)= √x

You can't take the square root of a negative number and get a real answer.  So x ≥ 0.  Then the range is (-∞, 0].  The square root returns a nonnegative value so the range is [0, ∞).

3.) f(x)= -x^2

I'm not sure if you wanted that minus sign squared or not, basically I'm wondering if the function is f(x) = -x² or if it is f(x) = (-x)².  In either case the domain is (-∞, ∞) because any number can be squared.  However the range is slightly different.  If the function is f(x) = -x² then the range is (-∞, 0] and if the function is f(x) = (-x)² then the range is [0, ∞) because squaring a number always makes it positive.

m(x)*n(x) =

(2x - 1)(x² + 2) =

Use FOIL (first, outer, inner, last) to multiply this

(2x)(x²) + (2x)(2) + (-1)(x²) + (-1)(2) =

2x³ + 4x - x² - 2 =

2x³ - x² + 4x - 2

f(x) - g(x) =

(3x² - 5x + 1) - (4x² + 9x - 2) =

3x² - 5x + 1 - 4x² - 9x + 2 =

3x² - 5x - 4x² - 9x + 3 =

3x² - 4x² - 5x - 9x + 3 =

3x² - 4x² - 14x + 3

Hope this helps you!