csat-suneung· South-Korea· csat__math-science3 marks
Two exponential functions $f ( x ) = a ^ { b x - 1 } , g ( x ) = a ^ { 1 - b x }$ satisfy the following conditions. (a) The graphs of the function $y = f ( x )$ and the function $y = g ( x )$ are symmetric with respect to the line $x = 2$. (b) $f ( 4 ) + g ( 4 ) = \frac { 5 } { 2 }$ What is the value of $a + b$, 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 the function $y = f ( x )$ and the function $y = g ( x )$ are symmetric with respect to the line $x = 2$.\\
(b) $f ( 4 ) + g ( 4 ) = \frac { 5 } { 2 }$
What is the value of $a + b$, 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) $\frac { 3 } { 2 }$