To Find: Determine the following values

a)$(f+g)\left(2\right)$

b)$(f-g)\left(12\right)$

c) (fg)(4)

d) (fg)(0)

a)

b)

c) (fg)(4)

d) (fg)(0)

slaggingV
2021-09-20
Answered

To Find: Determine the following values

a)$(f+g)\left(2\right)$

b)$(f-g)\left(12\right)$

c) (fg)(4)

d) (fg)(0)

a)

b)

c) (fg)(4)

d) (fg)(0)

You can still ask an expert for help

Caren

Answered 2021-09-21
Author has **96** answers

Given: The functions $f\left(x\right)=2x+1$ and $g\left(x\right)=1x$

We can define addition of two functions as follows

$(f+g)\left(x\right)=f\left(x\right)+g\left(x\right)$

We can define subtraction of two functions as follows

$(f-g)\left(x\right)=f\left(x\right)-g\left(x\right)$

We can define multiplication of two functions as follows

$\left(fg\right)\left(x\right)=f\left(x\right)\times g\left(x\right)$

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$(f+g)\left(x\right)=f\left(x\right)+g\left(x\right)$

Substituting f(x) and g(x) we get,

$(f+g)\left(x\right)=2x+1+1x$

Substituting$x=2$ we get,

$(f+g)\left(2\right)=2\left(2\right)+1+12$

$(f+g)\left(2\right)=5+12$

$(f+g)\left(2\right)=112$

b) Since$(f-g)\left(x\right)=f\left(x\right)-g\left(x\right)$

Substituting f(x) and g(x) we get,

$(f-g)\left(x\right)=2x+1-1x$

Substituting$x=12$ we get,

$(f-g)\left(12\right)=2\left(12\right)+1-112$

$(f-g)\left(12\right)=1+1-2$

$(f-g)\left(12\right)=0$

c) Since$\left(fg\right)\left(x\right)=f\left(x\right)g\left(x\right)$

Substituting f(x) and g(x) we get,

$\left(fg\right)\left(x\right)=(2x+1)\left(1x\right)$

Substituting$x=4$ we get,

$\left(fg\right)\left(4\right)=(2\times 4+1)\left(14\right)$

$\left(fg\right)\left(4\right)=\left(94\right)$

d) Since$\left(fg\right)\left(x\right)=f\left(x\right)g\left(x\right)$

Substituting f(X) and g(x) we get,

$\left(fg\right)\left(x\right)=(2x+1)\left(1x\right)$

We can define addition of two functions as follows

We can define subtraction of two functions as follows

We can define multiplication of two functions as follows

We can define division of two functions as follows

Calculation:

a) Since

Substituting f(x) and g(x) we get,

Substituting

b) Since

Substituting f(x) and g(x) we get,

Substituting

c) Since

Substituting f(x) and g(x) we get,

Substituting

d) Since

Substituting f(X) and g(x) we get,