Find the domain of the function
g(x)=3/10-7x
The domain of the function the way you typed it would be any real number for x
If you meant g(x) = 3/(10-7x)
then the domain is any real number except x ≠ 10/7
10 - 7 x # 0
10 # 7 x Divide both sides with 7
10 / 7 # x
x # 10 / 7
Domain:
( - infinity , 10 / 7 ] U [ 10 / 7 , infinity)
Remark:
# mean differently of
To find the domain of a function, we need to determine the values that x can take on such that the function is defined.
In this case, the function is defined for all values of x except the ones that make the denominator of the fraction equal to zero. The denominator of the fraction is 10 - 7x.
Setting the denominator equal to zero, we have:
10 - 7x = 0
To solve for x, we subtract 10 from both sides:
-7x = -10
Then, we divide both sides by -7 to isolate x:
x = -10 / -7
x = 10/7
Therefore, the only value of x that makes the denominator zero is x = 10/7.
Hence, the domain of the function g(x) = 3/(10 - 7x) is all real numbers except x = 10/7.