已知函数f(x)=αsinx+btanx+1满足f(5)=7,求f(-5)的值

题目

已知函数f(x)=αsinx+btanx+1满足f(5)=7,求f(-5)的值

答案

f(5)=αsin 5 + βtan 5 + 1 =7
所以,
αsin 5 + βtan 5 =6
αsin -5 + βtan -5 =-(αsin 5 + βtan 5)=-6
αsin -5 + βtan -5 +1 =-5
即 f（-5）=-5