JEE Main 2019 — Definite Integration Question with Solution
From: JEE Main 2019 (Online) 8th April Evening Slot
Question
Let where g is a non-zero even
function. If ƒ(x + 5) = g(x), then equals-
Choose an option
Show full solutionCorrect option: B
Correct answer
B
Step-by-step explanation
Put t = -v
=
= [ as g(v) is an even function.]
= - f(x)
f(-x) = -f(x)
f(x) is an odd function.
Given ƒ(x + 5) = g(x)
g(- x) = ƒ(- x + 5)
g(x) = - f(x - 5) [as g(x) is even and f(x) is an odd function]
Replacing x by x + 5, we get
f(x) = - g(x + 5) ......(1)
Now
=
=
=
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