Question

Determine the domain of the function. f as a function of x is equal to the square root of x plus one divided by x plus four times x minus six.


answers:
a) x ≥ -1, x ≠ 6
b) All real numbers except -4 and 6
c) All real numbers
d) x ≥ 0

Answer 1

Answer:

a) x ≥ -1 , x ≠ 6

Step-by-step explanation:

To quickly solve this problem, we can use a graphing tool or a calculator to plot the equation.

Please see the attached images below, to find more information about the graph

The correct answer is option

a) x ≥ -1 , x ≠ 6

Answer 2

Answer:

a) $x\geq -1,x\neq 6$

Step-by-step explanation:

We have been given a function $f(x)=\frac{\sqrt{x+1}}{(x+4)(x-6)}$. We are asked to find the domain of our given function.

We can see that our given function is a rational function and numerator of our given function is a square root.

To find the domain of our given function, we will find the number that will make our denominator 0 and the domain of square root function will be the values of x that will make our numerator non-negative.

Undefined points for our given function:

$(x+4)(x-6)=0$

$x+4=0\text{ or }x-6=0$

$x=-4\text{ or }x=6$  

The domain of denominator is all values of x, where x is not equal to negative 4 and positive 6.

Non negative values for radical:

$x+1\geq 0$

$x+1-1\geq 0-1$

$x\geq -1$

The domain of numerator is all value of x greater than or equal to negative

Upon combining real regions and undefined points for our given function, the domain of our given function will be all values of x greater than or equal to negative 1, where x is not defined for 6.

Therefore, domain of our given function is $x\geq -1,x\neq 6$.