let-f-x-g-x-and-h-x-be-functions-R-R-given-by-f-x-x-2-if-x-0-and-x-1-if-x-lt-0-g-x-x-2-4-if-x-2-and-1-2-x-if-x-lt-2-h-x-3-x-if-x-0-and-3-x-if-x-0-Calculate-f-2-f-g-2-f-g-h

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Question Number 74355 by Mr. K last updated on 22/Nov/19

$$letf\left(x\right),g\left(x\right)andh\left(x\right)befunctions$$$$\mathbb{R}\to \mathbb{R},givenby$$$$f\left(x\right)=x^2,ifx⩾0andx+1ifx<0$$$$g\left(x\right)=x^2-4,ifx⩾2and\frac{1}{2-x}ifx<2$$$$h\left(x\right)=3^{-x},ifx⩽0and{3}^{x}ifx⩾0$$$$Calculate\frac{f\left(2\right)+f\left(g\left(2\right)\right)}{f\left(g\left(h(-1)\right)\right)}.$$

Answered by MJS last updated on 23/Nov/19

$$\mathrm{easy}$$$$f\left(2\right)=4$$$$g\left(2\right)=0f\left(g\left(2\right)\right)=f\left(0\right)=0$$$$h(-1)=3g\left(h(-1)\right)=g\left(3\right)=5f\left(g\left(h(-1)\right)\right)=f\left(5\right)=25$$$$\frac{f\left(2\right)+f\left(g\left(2\right)\right)}{f\left(g\left(h(-1)\right)\right)}=\frac{4}{25}$$

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