Here,
[tex] f(x) = x^2 -3x+3 , g(x) = \frac{x-1}{4} [/tex]
And we need to find the value of f(g(x)) when x = 5 . It means , we need to find f(g(5)) .
So first we need to find g(5) and for that we plug 5 for x in g(x). That is ,
[tex] g(5)=\frac{5-1}{4}=1 [/tex]
So the value of g(5) is 1 .
Now we have f(g(5)) = f(1) . And f(1) is
[tex] 1^2 -3(1)+3 = 1 [/tex]
So the value of f(g(5)) =1
f(x)=x²-3x+3
g(x)=x-1/4
f(g(x))=f(x-1/4)
replacing x by x-1/4 in the function f(x),
f(g(x))=(x-1/4)²-3(x-1/4)+3
we have to find its value when x is 5, so
f(g(5))=(5-1/4)²-3(5-1/4)+3
= (4.75)²-14.25 +3
=22.5625 -11.25
f(g(5)) = 11.3125
