{ 1, x > 0 f …
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Sia ? 6 years ago
It is clear that gof : R {tex}\rightarrow{/tex} R and fog : R {tex}\rightarrow{/tex} R
Consider {tex}x = \frac{1}{2}{/tex} which lie on (0, # 1)
Now, {tex}(gof)\left( {\frac{1}{2}} \right) = g\left\{ {f\left( {\frac{1}{2}} \right)} \right\} {/tex} = g(1) = [1] = 1
And {tex}(fog)\left( {\frac{1}{2}} \right) = f\left\{ {g\left( {\frac{1}{2}} \right)} \right\} = f\left( {\left[ {\frac{1}{2}} \right]} \right){/tex} = f(0) = 0
{tex}\Rightarrow gof \ne fog{/tex} in (0, 1]
No, fog and gof don't coincide in (0, 1].
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