Let g(x)=2x and h(x)= x^2+4. FInd each value or expression (g*g)(a) & (h*h)(a)

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Since `g(x)=2x` , then the composition is:

`g circ g(a)`

`=g(g(a))`

`=g(2a)`  now sub in the function

`=2(2a)`  simplify

`=4a`

Also, since `h(x)=x^2+4` , the composition is:

`h circ h(a)`

`=h(h(a))`

`=h(a^2+4)`  sub in the function

`=(a^2+4)^2+4`  simplify the brackets

`=a^4+8a^2+16+4`  simplify the expression

`=a^4+8a^2+20`

The compositions are `g circ g(a)=4a` and `h circ h(a)=a^4+8a^2+20` .` `

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