csat-suneung 2009 Q8

csat-suneung · South-Korea · csat__math-humanities 3 marks Exponential Functions Parameter Determination from Conditions

Two exponential functions $f ( x ) = a ^ { b x - 1 } , g ( x ) = a ^ { 1 - b x }$ satisfy the following conditions.
(a) The graphs of $y = f ( x )$ and $y = g ( x )$ are symmetric with respect to the line $x = 2$.
(b) $f ( 4 ) + g ( 4 ) = \frac { 5 } { 2 }$
What is the value of the sum of the two constants $a + b$? (where $0 < a < 1$) [3 points]
(1) 1
(2) $\frac { 9 } { 8 }$
(3) $\frac { 5 } { 4 }$
(4) $\frac { 11 } { 8 }$
(5) $\frac { 3 } { 2 }$

Two exponential functions $f ( x ) = a ^ { b x - 1 } , g ( x ) = a ^ { 1 - b x }$ satisfy the following conditions.\\
(a) The graphs of $y = f ( x )$ and $y = g ( x )$ are symmetric with respect to the line $x = 2$.\\
(b) $f ( 4 ) + g ( 4 ) = \frac { 5 } { 2 }$

What is the value of the sum of the two constants $a + b$? (where $0 < a < 1$) [3 points]\\
(1) 1\\
(2) $\frac { 9 } { 8 }$\\
(3) $\frac { 5 } { 4 }$\\
(4) $\frac { 11 } { 8 }$\\
(5) $\frac { 3 } { 2 }$

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