Question

Given that f(x) =x^2 -3x+3 and g(x)= x-1/4, solve for f(g(x)), when x=5

A.) -3
B.)1
C.)7
D.)13

Answer 1

OK. First calculate g(5). Put the value of x to the equation of the function g(x):

`g(x)=x-(1)/(4)\to g(5)=5-(1)/(4)=4(3)/(4)=(19)/(4)`

Therefore
`f(g(x))=f\left((19)/(4)\right)`

Calculate:

`f(x)=x^2-3x+3\to f\left((19)/(4)\right)=\left((19)/(4)\right)^2-3\cdot(19)/(4)+3\\\\=(361)/(16)-(57)/(4)+3=(361)/(16)-(57\cdot4)/(4\cdot4)+(3\cdot16)/(16)\\\\=(361)/(16)-(228)/(16)+(48)/(16)=(361-228+48)/(16)\\\\=(181)/(16)`

hmmm... something is wrong. Maybe is
`g(x)=(x-1)/(4)`

Try:

`g(5)=(5-1)/(4)=(4)/(4)=1\\\\f(1)=1^2-3\cdot1+3=1-3+3=1`

Answer: B.) 1

Next time, remember to write your expressions correctly