Given:
The functions are,
h(x) = 4,
g(x) = x²+xsecx
The objective is to find which of the following is not known to be true.
Let's consider option (A).
[tex]\begin{gathered} (f\circ f^{-1}\circ h)(x)=(f(f^{-1})\circ h)(x) \\ =h(x) \\ =4 \end{gathered}[/tex]
Thus, option (A) is true.
Let's consider option (B).
[tex]\begin{gathered} (g\circ h\circ f^{-1})(x)=(g(h(x))f^{-1})(x) \\ =(g(4))f^{-1})(x) \\ =((4^2+4\sec 4)f^{-1})(x) \\ =((16+4\sec 4)f^{-1}(x)) \end{gathered}[/tex]
Since, the obtiaed answe doesn't matches with the given options.
Hence, option (B) is not true.
