Sets, Relations & Functions
Finding f(0) from Composite Function
nta_pyq_2023_apr
Grade 11
Question:
Let $f(g(x))=x+3-\sqrt{x}$ where $g(x)=\sqrt{x}+1$. Then $f(0)$ is equal to
Step-by-Step Solution
Key Concept: Substitute $g(x)=t$, so $\sqrt{x}=t-1$ and $x=(t-1)^2$. Then $f(t)=(t-1)^2+3-(t-1)$.
$f(t)=(t-1)^2+3-(t-1)$. $f(0)=1+3+1=5$.
Correct Answer: 2