Q. Let $f:\lbrack 4,\ \infty\lbrack \rightarrow \lbrack 4,\ \infty\lbrack$ be defined by $f(x) = 5^{x(x - 4)}$ then $f^{- 1}(x)$
A) $2 - \sqrt{4 + \log_{5}x}$
B) $2 + \sqrt{4 + \log_{5}x}$
C) $\left( \frac{1}{5} \right)^{x(x - 4)}$
D) Not defined
Explanation
(d)
Given, $f(x) = 5^{x(x - 4)}$ for $f:\lbrack 4,\ \infty\lbrack \rightarrow \lbrack 4,\ \infty\lbrack$
At $x = 4$
$\ \ \ \ \ \ \ \ \ \ \ f(x) = 5^{4(4 - 4)} = 1$
Which is not lie in the interval $\lbrack 4,\ \infty\lbrack$
$\therefore$ Function is not bijective.
Hence, $f^{- 1}(x)$ is not defined.
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.