f x gand f/g State any domain restricitions?
please help
2007-06-20 07:52:21 · 6 answers · asked by king 1 in Science & Mathematics ➔ Mathematics
5.
f(x) = 35x + 5
g(x)=5
f * g = (35x + 5)5
f * g = 175x + 25
f * g = 25(7x + 1)
f/g = (35x + 5) / 5
f/g = 5(7x + 1) / 5
f/g = 7x + 1
6.
f(x) = x^2 + 25
g(x) = 3x + 17
f * g = (x^2 + 25)(3x + 17)
f * g = 3x(x^2 + 25) + 17(x^2 + 25)
f * g = 3x^3 + 75x + 17x^2 + 425
f * g = 3x^3 + 17x^2 + 75x + 425
f/g = (x^2 + 25) / (3x + 17)
restriction
3x + 17 != 0 ( != means not equal)
3x != -17
x != -17/3
2007-06-20 08:03:13 · answer #1 · answered by topsyk 3 · 0⤊ 0⤋
5.) f*g(x)=(35x+5)*(5)=175x+25 no domain restrictions
f/g(x)=(35x+5)/(5)=7x+1 no domain restrictions
6.) f*g(x)=(x^2 + 25)*(3x+17)=3x^3+17x^2+75x+425 no domain restrictions
f/g(x)=(x^2 + 25)/(3x+17) x cannot be -17/3 as this would cause the denominator to be zero
when looking for domain restrictions you are assuming the domain is all reals and then eliminating any values that will cause a) a denominator of zero or b) a negative value under a radical (even root sign like square root, 4th root, etc)
2007-06-20 08:06:46 · answer #2 · answered by M K 2 · 0⤊ 0⤋
No, this is multiplication and division!
5) f * g = (35x + 5)(5) = 175x + 25
Linear function so domain is all real numbers.
f/g =(35x + 5)/5 = 7x + 1
Again, linear function so domain is all real numbers.
6) f * g = (x^2 + 25)(3x + 17) = 3x^3 + 17x^2 + 75x + 425
Polynomial function so domain is all real numbers
f/g = (x^2 + 25)/(3x + 17)
Can't have denominator equal to zero in a fraction so x cannot be -17/3.
2007-06-20 08:00:38 · answer #3 · answered by piggy30 3 · 0⤊ 0⤋
5.) There are no domain restrictions here for multiplication or division, you can plug in any real number for x and get a valid answer.
6.) f*g has no domain restrictions, but f/g does. In this case, g(x) cannot be 0. Thus, 3x + 17 /= 0 => x /= -17/3. The domain for f/g, therefore, is all real numbers x such that x is not equal to -17/3.
2007-06-20 08:01:23 · answer #4 · answered by GenoLV 2 · 0⤊ 0⤋
f(g(x)) = 45
f(x)/g(/x) = 7x+1 No domain restrictions
f(g(x)) = (3x+17)^2 +25= 9x^2 +102x + 314 No restrictions
f(x)/g(x) = x^2/(3x+17) Restriction: x not equal -17/3
2007-06-20 08:03:47 · answer #5 · answered by ironduke8159 7 · 0⤊ 0⤋
is that CALCULUS!!!?
2007-06-20 07:56:12 · answer #6 · answered by nightowl 2 · 0⤊ 1⤋