Question

The inverse function of $f(x) = ax + 1$, $x \in \mathbb{R}$ is itself. Then the value of $a$ is

• A. 1
• B. -1
• C. $\frac{1}{2}$
• D. $-\frac{1}{2}$
• E. 2

Hint:

Logic Tip: Graphically, a function that is its own inverse is symmetric about the line $y = x$. For a linear function $y = ax + b$ to be symmetric about $y = x$ (and not be the line $y=x$ itself), its slope $a$ must be $-1$.

Answer 1

The Correct Option is B