To Find: Determine the following values a) (f+g)(2) b) (f-g)

To Find: Determine the following values
a) $\left(f+g\right)\left(2\right)$
b) $\left(f-g\right)\left(12\right)$
c) (fg)(4)
d) (fg)(0)
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Caren
Given: The functions $f\left(x\right)=2x+1$ and $g\left(x\right)=1x$
We can define addition of two functions as follows
$\left(f+g\right)\left(x\right)=f\left(x\right)+g\left(x\right)$
We can define subtraction of two functions as follows
$\left(f-g\right)\left(x\right)=f\left(x\right)-g\left(x\right)$
We can define multiplication of two functions as follows
$\left(fg\right)\left(x\right)=f\left(x\right)×g\left(x\right)$
We can define division of two functions as follows
$\left(fg\right)\left(x\right)=f\left(x\right)g\left(x\right)$
Calculation:
a) Since $\left(f+g\right)\left(x\right)=f\left(x\right)+g\left(x\right)$
Substituting f(x) and g(x) we get,
$\left(f+g\right)\left(x\right)=2x+1+1x$
Substituting $x=2$ we get,
$\left(f+g\right)\left(2\right)=2\left(2\right)+1+12$
$\left(f+g\right)\left(2\right)=5+12$
$\left(f+g\right)\left(2\right)=112$
b) Since $\left(f-g\right)\left(x\right)=f\left(x\right)-g\left(x\right)$
Substituting f(x) and g(x) we get,
$\left(f-g\right)\left(x\right)=2x+1-1x$
Substituting $x=12$ we get,
$\left(f-g\right)\left(12\right)=2\left(12\right)+1-112$
$\left(f-g\right)\left(12\right)=1+1-2$
$\left(f-g\right)\left(12\right)=0$
c) Since $\left(fg\right)\left(x\right)=f\left(x\right)g\left(x\right)$
Substituting f(x) and g(x) we get,
$\left(fg\right)\left(x\right)=\left(2x+1\right)\left(1x\right)$
Substituting $x=4$ we get,
$\left(fg\right)\left(4\right)=\left(2×4+1\right)\left(14\right)$
$\left(fg\right)\left(4\right)=\left(94\right)$
d) Since $\left(fg\right)\left(x\right)=f\left(x\right)g\left(x\right)$
Substituting f(X) and g(x) we get,
$\left(fg\right)\left(x\right)=\left(2x+1\right)\left(1x\right)$