Consider the function f(x)=12x+√2.f(x)=12x+√2.f(x)=12x+√2. Find the value of √2[f(−5)+f(−4)+f(−3)+f(−2)+f(−1)+f(0)+f(1)+f(2)+f(3)+f(4)+f(5)+f(6)].√2[f(−5)+f(−4)+f(−3)+f(−2)+f(−1)+f(0)+f(1)+f(2)+f(3)+f(4)+f(5)+f(6)].√2[f(−5)+f(−4)+f(−3)+f(−2)+f(−1)+f(0)+f(1)+f(2)+f(3)+f(4)+f(5)+f(6)].
Answer:
666
- Given, f(x)=12x+√2f(x)=12x+√2f(x)=12x+√2
Here, f(−5)f(−5)f(−5) can be written asf(1−6).f(1−6).f(1−6).
Similarly, f(−4)=f(1−5),f(−3)=f(1−4), …f(0)=f(1−1)f(−4)=f(1−5),f(−3)=f(1−4), …f(0)=f(1−1)f(−4)=f(1−5),f(−3)=f(1−4), …f(0)=f(1−1) - We have
[Math Processing Error] - Now,
[Math Processing Error] - Hence, the value of the given expression is 6.6.