Question

Which of the following are the appropriate LaTeX: f\left(x\right)f ( x ) and LaTeX: g\left(x\right)g ( x ), for LaTeX: H\left(x\right)=\cos\left(2x^2-1\right)H ( x ) = cos ⁡ ( 2 x 2 − 1 ) for LaTeX: H\left(x\right)=\left(f\:\circ\:g\right)\left(x\right)H ( x ) = ( f ∘ g ) ( x )? Group of answer choices

Answer 1

Answer:

$f\left(x\right)=\cos\left(x\right)\: and\:\: g\left(x\right)=\left(2x^2-1\right)$

Step-by-step explanation:

We have, $H\left(x\right)=\cos\left(2x^2-1\right)H ( x )$

                          $=\cos\left(2x^2-1\right)$

And   $H\left(x\right)=\left(f\:\circ\:g\right)\left(x\right)H ( x ) = \left(f\:\circ\:g\right)( x )$

        $\Rightarrow \left(f\:\circ\:g\right)(x)=\cos\left(2x^2-1\right)$

Now, $f\left(x\right)=\cos\left(x\right)$   and $g\left(x\right)=\left(2x^2-1\right)$