Sets, Relations & Functions
Functions
star_batch_jee_advanced_2025
Grade 11
Question:
Let $f(x)$ be any function. The graphs of $y = f(x-1)$ and $y = f(-x+1)$ are symmetric about the line:
$y = 0$
$x = 0$
$x = 1$
$x = -1$
Step-by-Step Solution
Key Concept: Function symmetry about a vertical line $x=a$ occurs when $f(a+t) = f(a-t)$.
Since $-(x-1) = -x+1$, the graphs of $f(x)$ and $f(-(x-1))$ are symmetric about the line $x-1=0$ or $x=1$.
Correct Answer: 3