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

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

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)`