Hyperbola
Composition of Functions (appears in Hyperbola PDF)
nta_pyq_2023_jan
Grade 11
Question:
For some $a, b, c \in \mathbb{N}$, let $f(x) = ax - 3$ and $g(x) = x^b + c$, $x \in \mathbb{R}$. If $(f \circ g)^{-1}(x) = \left(\dfrac{x-7}{2}\right)^{1/3}$, then $(f \circ g)(ac) + (g \circ f)(b)$ is equal to ______.
Step-by-Step Solution
Key Concept: Find $a,b,c$ from $fog(x)=2x^3+7$; compute $fog(10)$ and $gof(3)$.
$a=2,b=3,c=5$. $fog(10)=2(10)^3+7=2007$; $gof(3)=(2\cdot3-3)^3+5=32$. Sum $=2039$.
Correct Answer: 2039