SOLUTION: for f(x)=3x^2+5 and g(x)=7x-2, a)verify:g(x+2)not equal to g(x)+g(2). b)find(f-g)(x). c) using the resulting function in (b), show that (f-g)(2)=f(2)-g(2). d)is (fg)(0)= (f/g)(

Algebra ->  Functions -> SOLUTION: for f(x)=3x^2+5 and g(x)=7x-2, a)verify:g(x+2)not equal to g(x)+g(2). b)find(f-g)(x). c) using the resulting function in (b), show that (f-g)(2)=f(2)-g(2). d)is (fg)(0)= (f/g)(      Log On


   

Question 947948: for f(x)=3x^2+5 and g(x)=7x-2,
a)verify:g(x+2)not equal to g(x)+g(2).
b)find(f-g)(x).
c) using the resulting function in (b), show that (f-g)(2)=f(2)-g(2).
d)is (fg)(0)= (f/g)(0)?explain.
e)find f(x+h)-f(x)/h,h is not equal to 0
Answer by MathLover1(20855) About Me  (Show Source):
You can put this solution on YOUR website!

for f%28x%29=3x%5E2%2B5 and g%28x%29=7x-2,
a)
verify:
g%28x%2B2%29%3C%3Eg%28x%29%2Bg%282%29
7%28x%2B2%29-2%3C%3E7x-2%2B7%282%29-2
7x%2B14-2%3C%3E7x-2%2B14-2
7x%2B12%3C%3E7x%2B10
b)
find %28f-g%29%28x%29
%28f-g%29%28x%29=f%28x%29-g%28x%29+
%28f-g%29%28x%29=3x%5E2%2B5-%287x-2%29
%28f-g%29%28x%29=3x%5E2%2B5-7x%2B2
%28f-g%29%28x%29=f%28x%29-g%28x%29+=3x%5E2-7x%2B7
c)
using the resulting function in (b), show that
%28f-g%29%282%29=f%282%29-g%282%29
3%282%29%5E2-7%2A2%2B7=3%282%29%5E2%2B5-%287%282%29-2%29
3%2A4-14%2B7=3%2A4%2B5-%2814-2%29
12-14%2B7=12%2B5-%2812%29
19-14=17-12
5=5
d)
is %28fg%29%280%29=+%28f%2Fg%29%280%29? explain
%283%2A0%5E2%2B5%29%287%2A0-2%29=+%28%283%2A0%5E2%2B5%29%2F%287%2A0-2%29%29
%280%2B5%29%280-2%29=+%28%280%2B5%29%2F%280-2%29%29
%285%29%28-2%29=+5%2F-2
-10%3C%3E+5%2F-2
both f%28x%29=3x%5E2%2B5 and g%28x%29=7x-2 have y-intercept; so, if x=0 then f%28x%29=3x%5E2%2B5 will be equal to 5 , and g%28x%29=7x-2 will be equal to -2
e)
find %28f%28x%2Bh%29-f%28x%29%29%2Fh, h is not equal to 0
%283%28x%2Bh%29%5E2%2B5-%283%28x%2Bh%29%5E2%2B5%29%29%2Fh
%283%28x%5E2%2B2xh%2Bh%5E2%29%2B5-%283%28x%5E2%2B2xh%2Bh%5E2%29%2B5%29%29%2Fh
%283x%5E2%2B6xh%2Bh%5E2%2B5-%283x%5E2%2B6xh%2B3h%5E2%29%2B5%29%2Fh

0%2Fh
0