For a general role \$f\$, which have the right to be about anything and also is \$cos\$ in her case and with \$g(x)=x^n\$,\$\$f^n(x) := (f(x))^n = gcirc f(x) = g(f(x))\$\$and\$\$f(x^n) := f(underbracexcdot x cdot ldots_n ext times) = f circ g(x) = f(g(x))\$\$are two various functions.Note for trigonometric functions, \$cos^-1\$ periodically refers come \$arccos\$, and sometimes to \$sec = frac1cos\$, so you should be careful around exponentiating functions.

You are watching: (cos(x))^2 One that the first things you might observe is the \$(cos small(xsmall))^2geqslant0\$ vice versa, \$cos(x^2)\$ might be equal to a negative number. (Why?)

In blue, a graph of the duty \$colorbluecos^2(x)\$ and in red a graph of the function \$colorredcos(x^2)\$. Some say, a an excellent plot is worth a million words! :-)

There are couple of functions such that \$f^2(x)=f(x^2)\$: basically the powers of \$x\$, \$f(x)=x^n\$: \$f^2(x)=(x^n)^2=(x^2)^n=f(x^2)\$.

The preeminence is more often \$f^2(x) e f(x^2)\$. Just an example with\$f(x)=x+1\$: \$(x+1)^2 e x^2+1\$.    Thanks because that contributing response to ptcouncil.net Stack Exchange!

But avoid

Asking for help, clarification, or responding to other answers.Making statements based upon opinion; ago them increase with references or an individual experience.

Use ptcouncil.netJax to layout equations. ptcouncil.netJax reference.

See more: How Much Mac And Cheese Per Person, Macaroni And Cheese For 20