SOLUTION: Give f(x)=3x^2+4x-1 and g(x)=x+3 simplify the expression when possible f(-3) (g degree sign f)(-1/2) here are the choices: a. 111/4 b.-9/4 c.-3/2 d.3/4 any help woul

Algebra ->  Equations -> SOLUTION: Give f(x)=3x^2+4x-1 and g(x)=x+3 simplify the expression when possible f(-3) (g degree sign f)(-1/2) here are the choices: a. 111/4 b.-9/4 c.-3/2 d.3/4 any help woul      Log On


   

Question 189559: Give f(x)=3x^2+4x-1 and g(x)=x+3 simplify the expression when possible
f(-3)
(g degree sign f)(-1/2)
here are the choices:
a. 111/4
b.-9/4
c.-3/2
d.3/4
any help would be appreciated thanks so much!
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%28g+o+f%29%28-1%2F2%29 Start with the given expression.


g%28f%28-1%2F2%29%29 Expand. Note: %28g+o+f%29%28x%29=g%28f%28x%29%29



So we first need to evaluate f%28-1%2F2%29


f%28x%29=3x%5E2%2B4x-1 Start with the given function


f%28-1%2F2%29=3%28-1%2F2%29%5E2%2B4%28-1%2F2%29-1 Plug in x=-1%2F2


f%28-1%2F2%29=3%281%2F4%29%2B4%28-1%2F2%29-1 Square -1%2F2 to get 1%2F4


f%28-1%2F2%29=3%2F4-4%2F2-1 Multiply


f%28-1%2F2%29=3%2F4-2-1 Reduce


f%28-1%2F2%29=3%2F4-8%2F4-4%2F4 Multiply the second and third term by 4%2F4 (to get the denominators equal)


f%28-1%2F2%29=%283-8-4%29%2F4 Combine the fractions


f%28-1%2F2%29=-9%2F4 Combine like terms.


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g%28x%29=x%2B3 Move onto the second function


g%28f%28-1%2F2%29%29=-9%2F4%2B3 Plug in f%28-1%2F2%29=-9%2F4


g%28f%28-1%2F2%29%29=-9%2F4%2B12%2F4 Multiply the second term by 4%2F4 to get the denominators equal.


g%28f%28-1%2F2%29%29=%28-9%2B12%29%2F4 Combine the fractions


g%28f%28-1%2F2%29%29=3%2F4 Combine like terms.



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Answer:

So %28g+o+f%29%28-1%2F2%29=3%2F4 which means that the answer is D)