Question

Let a = ${\sin }^{-1}\left(\sin 3\right)+{\sin }^{-1}\left(\sin 4\right)+{\sin }^{-1}\left(\sin 5\right),f\left(x\right)=e^{x{}^2+|x|}$ domain of $f\left(x\right)$ be $[a,\infty )$ &-range of $f\left(x\right)$ be $[b,\infty )$ and $g\left(x\right)=[4\cos {}^{4}x-2\cos 2x-\frac{1}{2}\cos 4x-x{}^7{]}^{\frac{1}{7}}$ domain & range of $g\left(x\right)$ is set of real numbers.
Which of the following are correct?

• A. $a=-2$
• B. $a+b=-1$
• C. $f\left(g\right(g\left(b\right)\left)\right)=e^2$
• D. $Bothf\left(x\right),g\left(x\right)arenoninvertiblefunctions$

Answer 1

Answer: (A), (B), (C)

The correct options are
A $a=-2$
B $a+b=-1$
C $f\left(g\right(g\left(b\right)\left)\right)=e^2$