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Determine the domain and range of the function

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Determine the domain and range of the function f%28x%29+=+%28x%5E2%2B15x-56%29%2F%28x%5E2%2B3x%2B2%29.

asked Mar 14, 2014 in ALGEBRA 1 by mathgirl Apprentice

3 Answers

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The function is f(x) = (x2 + 15x - 56)/(x2 + 3x + 2).

Domain :

Domain of a function f(x) is set of those values of x which will make the function mathematically legal or correct..certain operations like division by zero , square root of a negative number do not exist in real maths.

1. Domain excludes x - values that result in division by zero.

2. Domain excludes x - values that result in even roots of negative numbers.

Find the factors of numerator expression x2 + 15x - 56.

The above expression cannot be write in factorization form, since the any two numbers does not adjusted in their sum 15 and their product - 56.

Find the factors of denominator expression x2 + 3x + 2.

= x2 + 3x + 2

= x2 + 2x + x + 2

= x(x + 2) + 1(x + 2)

= (x + 1)(x + 2).

f(x) = (x2 + 15x - 56) / [(x + 1)(x + 2)].

The denominator expression is (x + 1)(x + 2) and it is equals to zero.

(x + 1)(x + 2) = 0

x = - 1 and x = - 2.

The denominator is zero, when x = - 1 and x = - 2.

Domain excludes x - values that result in division by zero.

The function has an implied domain that consists of all real x other than x = - 1 and x = - 2.These values are excluded from the domain because division by zero is undefined.

Domain : {x Є R : x ≠ - 2 and x ≠ - 1}.

answered Apr 4, 2014 by steve Scholar
+1 vote

To determine the range of f (x ) = image

To find the range, we want to find all yy  for which there exists an x such that image

  • Step-1

y = 0 in our range

To find x intercept let the numarator = 0

image

Compare it to image

image

image

image

image

image

image

answered Jun 16, 2014 by david Expert
+1 vote

Contiuous...

  • Step-2

image

image

image

image

We can solve this equation for x

If y not equals to 0, this is a quadratic equation in x ,so we can sole it with the quadratic formula:

Compare it to image

a = y-1 , b = 3y - 15, c = 2y + 56.

Roots are image

image

image

So,for a given y, y is in the range if this expression yields a real number.That is if image

image

image

image

image

image

image

image

We exclude y = 0 earlier , but we know y = 0 in our range

Thus the range of f(x)= image 

.

answered Jun 16, 2014 by david Expert

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