Addition and Subtraction of Function

Which of the following represents the sum of two functions f(x) and g(x)?

• $f\left(x\right)+g\left(x\right)$

• $f\left(x\right)-g\left(x\right)$

• $f\left(x\right)\cdot g\left(x\right)$

• $f\left(g\left(x\right)\right)$

The following expressions represent the difference of two functions f(x) and g(x) except ____________.

• $\left(g-f\right)\left(x\right)$

• $g\left(x\right)-f\left(x\right)$

• $\left(f-g\right)\left(x\right)$

• $g\left(f\left(-x\right)\right)$

Determine the validity of the statement " $f(x)−g(x)$ 
 is the same as  $g(x)−f(x)$ ". 

• always true

• sometimes true

• never true

• cannot be determined

What is $\left(f-g\right)\left(x\right)$ if  $f\left(x\right)=5x-3$  and  $g\left(x\right)=15x+6$  ?

•  $-10x-9$  

•  $-10x+9$  

•  $10x+9$  

•  $10x-9$  

If $g\left(x\right)=-7x-1$ and  $h\left(x\right)=2x+3$ , what is  $\left(g+h\right)\left(x\right)$ ?

•  $-5x+2$  

•  $9x+6$  

•  $15x-6$  

•  $-19x+5$  

If $g\left(x\right)=5x^2-3x+1$ and  $h\left(x\right)=5-5x-7x^2$ , what is  $\left(h-g\right)\left(x\right)$  

•  $12x^2+2x+4$  

•  $-12x^2+2x+4$  

•  $12x^2-2x-4$  

•  $-12x^2-2x+4$  

What is  $f\left(\sqrt{2}\right)+g\left(\sqrt{3}\right)$ if  $f\left(x\right)=5x^2-x+5$  and  $g\left(x\right)=3x^2+2x-1$ ?

•  $23-\sqrt{2}+2\sqrt{3}$  

•  $23+\sqrt{2}-2\sqrt{3}$  

•  $23-\sqrt{5}$  

•  $23+\sqrt{5}$  

Vincent's father will celebrate his birthday next month. Vincent saved  $f(x)=(2x^2+10x+3)$  pesos from his allowance to buy a gift that costs  $g(x)=(3x+7)$   pesos. How much did he still have after buying

•  $\left(2x^2+13x+10\right)\ pesos$  

•  $\left(2x^2-13x+10\right)\ pesos$  

•  $\left(2x^2+7x-4\right)\ pesos$  

•  $\left(2x^2-7x+4\right)\ pesos$  

The HR Department informed Benelyn that her starting salary as car sales agent will be $f(x)=(10x^2−5x+12)$ pesos. She will receive  $g(x)=(2x^2+3x−5)$ pesos as incentive if she is able to meet the quota after six months. What will be her new salary after six months, assuming that she meets the quota?

•  $\left(12x^2-2x+7\right)\ pesos$  

•  $\left(12x^2+2x+7\right)\ pesos$  

•  $\left(12x^2-2x-7\right)\ pesos$  

•  $\left(12x^2+2x-7\right)\ pesos$  

Elvince weighs  $f(x)=(5x^2+5x+3)$  pounds. What will be his weight after he loses  $g(x)=(2x^2−2x+1)$  
 pounds?

•  $\left(3x^2-3x-2\right)\ pounds$  

•  $\left(3x^2-3x-4\right)\ pounds$  

•  $\left(3x^2-7x-2\right)\ pounds$  

•  $\left(3x^2-7x-4\right)\ pounds$