OK. First calculate g(5). Put the value of x to the equation of the function g(x):
[tex]g(x)=x-\dfrac{1}{4}\to g(5)=5-\dfrac{1}{4}=4\dfrac{3}{4}=\dfrac{19}{4}[/tex]
Therefore [tex]f(g(x))=f\left(\dfrac{19}{4}\right)[/tex]
Calculate:
[tex]f(x)=x^2-3x+3\to f\left(\dfrac{19}{4}\right)=\left(\dfrac{19}{4}\right)^2-3\cdot\dfrac{19}{4}+3\\\\=\dfrac{361}{16}-\dfrac{57}{4}+3=\dfrac{361}{16}-\dfrac{57\cdot4}{4\cdot4}+\dfrac{3\cdot16}{16}\\\\=\dfrac{361}{16}-\dfrac{228}{16}+\dfrac{48}{16}=\dfrac{361-228+48}{16}\\\\=\dfrac{181}{16}[/tex]
hmmm... something is wrong. Maybe is [tex]g(x)=\dfrac{x-1}{4}[/tex]
Try:
[tex]g(5)=\dfrac{5-1}{4}=\dfrac{4}{4}=1\\\\f(1)=1^2-3\cdot1+3=1-3+3=1[/tex]
Answer: B.) 1
Next time, remember to write your expressions correctly
