Question 189559
{{{(g o f)(-1/2)}}} Start with the given expression.



{{{g(f(-1/2))}}} Expand. Note: {{{(g o f)(x)=g(f(x))}}}




So we first need to evaluate {{{f(-1/2)}}}



{{{f(x)=3x^2+4x-1}}} Start with the given function



{{{f(-1/2)=3(-1/2)^2+4(-1/2)-1}}} Plug in {{{x=-1/2}}}



{{{f(-1/2)=3(1/4)+4(-1/2)-1}}} Square {{{-1/2}}} to get {{{1/4}}}



{{{f(-1/2)=3/4-4/2-1}}} Multiply



{{{f(-1/2)=3/4-2-1}}} Reduce



{{{f(-1/2)=3/4-8/4-4/4}}} Multiply the second and third term by {{{4/4}}} (to get the denominators equal)



{{{f(-1/2)=(3-8-4)/4}}} Combine the fractions



{{{f(-1/2)=-9/4}}} Combine like terms.



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{{{g(x)=x+3}}} Move onto the second function



{{{g(f(-1/2))=-9/4+3}}} Plug in {{{f(-1/2)=-9/4}}}



{{{g(f(-1/2))=-9/4+12/4}}} Multiply the second term by {{{4/4}}} to get the denominators equal.



{{{g(f(-1/2))=(-9+12)/4}}} Combine the fractions



{{{g(f(-1/2))=3/4}}} Combine like terms.




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Answer:


So {{{(g o f)(-1/2)=3/4}}} which means that the answer is D)