57. Find the domain of:
y= 5
_____
2x+24
a. all real numbers except 12
b. all real numbers except 0.08
c. all real numbers except -0.08
d. all real numbers except -12
I still don't get how to do these, and this one looks even more complicated than the others.
if x is -12, what is the denominator? Is that allowed?
OH, so it's all real numbers except -12
To find the domain of a function, you need to determine the values of x for which the function is defined. In other words, you are looking for any restrictions or limitations on the variable x.
In this case, you have the function y = 5 / (2x + 24). The only restriction or limitation you need to consider is when the denominator (2x + 24) equals zero. This is because dividing by zero is undefined in mathematics.
To find the value of x that makes the denominator zero, you can set 2x + 24 = 0 and solve for x:
2x + 24 = 0
2x = -24
x = -24/2
x = -12
Therefore, x = -12 is the value that makes the denominator zero. This means that the function is undefined at x = -12.
Now, let's examine the options:
a. all real numbers except 12
b. all real numbers except 0.08
c. all real numbers except -0.08
d. all real numbers except -12
Since the function is undefined at x = -12, the correct answer is option d: all real numbers except -12. This is because all other options do not take into account the restriction at x = -12.
Remember, when determining the domain of a function, you need to identify any values of x that make the function undefined and exclude them from the domain.