FobelloE

2021-09-12

Values of the following expressions:
a) $\left(g\cdot f\right)\left(0\right)$
b) $\left(f\cdot g\right)\left(5\right)$
c) $\left(g\cdot g\right)\left(10\right)$

FieniChoonin

Given:
The table of values for two functions:
$\begin{array}{|ccccc|}\hline x& 0& 5& 10& 15\\ f\left(x\right)& 5& 0& 10& 15\\ \hline\end{array}$
$\begin{array}{|ccccc|}\hline x& 0& 5& 10& 15\\ g\left(x\right)& 15& 10& 5& 0\\ \hline\end{array}$
Formula used:
Composition of functions is defined as: $\left(f\cdot g\right)\left(x\right)=f\left(g\left(x\right)\right)$
Calculation:
Upon using the definition of composition functions and plugging the required values, we get:
a) $\left(g\cdot f\right)\left(0\right)=g\left(f\left(0\right)\right)=g\left(5\right)=10$
b) $\left(f\cdot g\right)\left(5\right)=f\left(g\left(5\right)\right)=f\left(10\right)=10$
c) $\left(g\cdot g\right)\left(10\right)=g\left(g\left(10\right)\right)=g\left(5\right)=10$
Conclusion:
a) $\left(g\cdot f\right)\left(0\right)=10$
b) $\left(f\cdot g\right)\left(5\right)=10$
c) $\left(g\cdot g\right)\left(10\right)=10$

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