OG详解-OG4 数学1 Q27

The correct answer is 5. It’s given that f (x )= -ax + b. Substituting -a^x + b for f (x) in the equation y = f (x)-15 yields y = -a^x + b -15. It’s given that the y-intercept of the graph of y = f (x)-15 is (0, - 997​​). Substituting 0 for x and -997​for y in the equation y = -a^x + b -15 yields - 997​​= -a⁰ + b -15, which is equivalent to -997​​ =-1+ b -15, or - 997​​ = b -16. Adding 16 to both sides of this equation yields 13​7​= b. It’s given that the product of a and b is 65​7​, or ab = 65​7. Substituting 13​7​ for b in this equation yields (a)(13​7​)=65​7​. Dividing both sides of this equation by 13​7​yields a = 5.