csat-suneung 2021 Q18

csat-suneung · South-Korea · csat__math-science 4 marks Curve Sketching Continuity and Discontinuity Analysis of Piecewise Functions

For a constant $a$, define the function $f ( x )$ as $$f ( x ) = \lim _ { n \rightarrow \infty } \frac { ( a - 2 ) x ^ { 2 n + 1 } + 2 x } { 3 x ^ { 2 n } + 1 }$$ What is the sum of all values of $a$ such that $( f \circ f ) ( 1 ) = \frac { 5 } { 4 }$? [4 points]
(1) $\frac { 11 } { 2 }$
(2) $\frac { 13 } { 2 }$
(3) $\frac { 15 } { 2 }$
(4) $\frac { 17 } { 2 }$
(5) $\frac { 19 } { 2 }$

For a constant $a$, define the function $f ( x )$ as
$$f ( x ) = \lim _ { n \rightarrow \infty } \frac { ( a - 2 ) x ^ { 2 n + 1 } + 2 x } { 3 x ^ { 2 n } + 1 }$$
What is the sum of all values of $a$ such that $( f \circ f ) ( 1 ) = \frac { 5 } { 4 }$? [4 points]\\
(1) $\frac { 11 } { 2 }$\\
(2) $\frac { 13 } { 2 }$\\
(3) $\frac { 15 } { 2 }$\\
(4) $\frac { 17 } { 2 }$\\
(5) $\frac { 19 } { 2 }$

Paper Questions

Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10 Q11 Q12 Q13 Q14 Q15 Q16 Q17 Q18 Q19 Q20 Q21 Q22 Q23 Q24 Q25 Q26 Q27 Q28 Q29