Need help with the composition of functions. I have attached a screenshot of the question.
1 answer:
So,
To compose a function with another, substitute the inside function into every place where x appears in the outer function.
For (h * h)(x), substitute h(x) for every x in the outer function, h(x).
![h(x)=\frac{6}{x}-->(h^oh)(x)=\frac{6}{\frac{6}{x}}=6*\frac{x}{6}=x](https://tex.z-dn.net/?f=h%28x%29%3D%5Cfrac%7B6%7D%7Bx%7D--%3E%28h%5Eoh%29%28x%29%3D%5Cfrac%7B6%7D%7B%5Cfrac%7B6%7D%7Bx%7D%7D%3D6%2A%5Cfrac%7Bx%7D%7B6%7D%3Dx)
For (f * f)(x), substitute f(x) for every x in the outer function, f(x).
![f(x)=x^2-5-->(f^of)(x)=(x^2-5)^2-5=x^4-10x^2+20](https://tex.z-dn.net/?f=f%28x%29%3Dx%5E2-5--%3E%28f%5Eof%29%28x%29%3D%28x%5E2-5%29%5E2-5%3Dx%5E4-10x%5E2%2B20)
Hope this helps!
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