for the given functions f and g find the following and state the domain of each result
f(x)=3x+1/8x-9; g(x)=5x/8x-9
A) (f+g)(x)=?
B)domain of (f+g)
c) (f/g)(x)=?
d) domain of f/g?
please show work
assuming you mean
f(x) = (3x+1)/(8x-9)
g(x) = 5x/(8x-9)
(f+g)(x) = [(3x+1)+5x]/(8x-9) = (8x+1)/(8x-9)
(f/g)(x) = (3x+1)/(8x-9) * (8x-9)/5x = (3x+1)/5x
domain is all reals except where the denominator is zero.
visit wolframalpha.com and type
plot <function>
to see a graph of <function>
That should help you get a handle on the range
ok genius, When you type fast sometimes it happens...move along!
To find (f+g)(x), we need to find the sum of the functions f(x) and g(x).
A) (f+g)(x) = f(x) + g(x)
= (3x + 1)/(8x - 9) + (5x)/(8x - 9)
= (3x + 5x + 1)/(8x - 9)
= (8x + 1)/(8x - 9)
To find the domain of (f+g), we need to determine the values of x for which the function is defined. In this case, the function (f+g)(x) is defined except when the denominator (8x - 9) equals zero since division by zero is undefined.
B) Domain of (f+g):
8x - 9 ≠ 0
x ≠ 9/8
Therefore, the domain of (f+g) is all real numbers except x = 9/8.
To find (f/g)(x), we need to divide the function f(x) by g(x).
C) (f/g)(x) = f(x) / g(x)
= (3x + 1)/(8x - 9) / (5x)/(8x - 9)
= (3x + 1)/(8x - 9) * (8x - 9)/(5x)
= (3x + 1)/(5x)
To find the domain of (f/g), we need to determine the values of x for which the function is defined. In this case, the function (f/g)(x) is defined except when the denominator (5x) equals zero since division by zero is undefined.
D) Domain of (f/g):
5x ≠ 0
x ≠ 0
Therefore, the domain of (f/g) is all real numbers except x = 0.
To find the results of (f+g)(x) and (f/g)(x), we need to perform the given operations on the functions f(x) and g(x).
Let's start with (f+g)(x), which means adding the functions f(x) and g(x).
A) (f+g)(x) = f(x) + g(x)
Substituting the given functions:
(f+g)(x) = (3x+1)/(8x-9) + (5x)/(8x-9)
To add these fractions, we need a common denominator, which is (8x-9).
(f+g)(x) = (3x+1 + 5x)/(8x-9)
Simplifying the numerator:
(f+g)(x) = (8x+1)/(8x-9)
Therefore, the result of (f+g)(x) is (8x+1)/(8x-9).
B) To find the domain of (f+g), we need to identify any values of x that would make the denominator zero, as division by zero is undefined. In this case, the denominator is 8x-9.
Setting the denominator equal to zero:
8x - 9 = 0
Solving for x:
8x = 9
x = 9/8
So, the domain of (f+g) is all real numbers except x = 9/8.
For (f/g)(x), we need to divide f(x) by g(x).
C) (f/g)(x) = f(x)/g(x)
Substituting the given functions:
(f/g)(x) = (3x+1)/(8x-9) / (5x)/(8x-9)
To divide fractions, we multiply the first fraction by the reciprocal of the second fraction:
(f/g)(x) = (3x+1)/(8x-9) * (8x-9)/(5x)
Simplifying:
(f/g)(x) = (3x+1)/(5x)
Therefore, the result of (f/g)(x) is (3x+1)/(5x).
D) To find the domain of (f/g), we need to identify any values of x that would make the denominator zero, as division by zero is undefined. In this case, the denominator is 5x.
Setting the denominator equal to zero:
5x = 0
Solving for x:
x = 0
So, the domain of (f/g) is all real numbers except x = 0.