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Let f:R→R:f(x)=(x+1) and g:R→R:g(x)=(x^2...

Let `f:R→R:f(x)=(x+1)` and `g:R→R:g(x)=(x^2 −4)`. Write down the formulae for `(fog)`.

Text Solution

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`f(x)=[x^(2)-x-1],x in[-1,2]`
Let us first draw the graph of `y=x^(2)-x-1`, which is an upward parabola having vertex at (1/2,-5/4).

The graph of `f(x)=[x^(2)-x-1]` can be drawn as shown in the following figure.

From the figure, `y=f(x)` is discontinuous at `x=-1,0,2 and the values of x for which `x^(2)-x-1=0orx=(1pmsqrt5)/(2)`.
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