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Question Number 39671 by KMA last updated on 09/Jul/18

$$Threefunctionaregivenf\left(x\right)=\sqrt{x}$$$$g\left(x\right)=x+5andh\left(x\right)=x^2+5.Express$$$$h\left(x\right)intermsoff\left(x\right)andg\left(x\right).$$

Answered by MrW3 last updated on 10/Jul/18

$$h\left(x\right)=x^2+5=x^2-x+x+5=x(x-1)+(x+5)$$$$\Rightarrow h\left(x\right)=f^2\left(x\right)[f^2\left(x\right)-1]+g\left(x\right)$$$$or$$$$h\left(x\right)=f^4\left(x\right)+5$$

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