Respuesta :
Combining various functions at different operations:
A.) Sum of Two Functions
[tex](f\text{ + g)(x) = }f(x)\text{ + g(x)}[/tex]In adding two functions, you add their output of the functions
Example: f(x) = x + 1 and g(x) = x + 2
(f + g)(x) = f(x) + g(x) = (x + 1) + (x + 2) = x + 1 + x + 2 = 2x + 3
(f + g)(1) = f(1) + g(1) = (1 + 1) + (1 + 2) = 2 + 3 = 5
B.) Subtraction of Two Functions
[tex](f\text{ - g)(x) = f(x) - g(x)}[/tex]In subtracting two functions, you subtract the output of the functions.
Example: f(x) = x + 1 and g(x) = x + 2
(f - g)(x) = f(x) - g(x) = (x + 1) - (x + 2) = x + 1 - x - 2 = -1
(f - g)(1) = f(x) - g(x) = (1 + 1) - (1 + 2) = 2 - 3 = -1
C.) Multiplication of Two Functions
[tex]\mleft(f\cdot g\mright)\mleft(x\mright)=f\mleft(x\mright)\cdot g\mleft(x\mright)[/tex]In multiplying two functions, you multiply the output of the functions.
Example: f(x) = x + 1 and g(x) = x + 2
(f * g)(x) = f(x) * g(x) = (x + 1) * (x + 2) = x^2 + 2x + x + 2 = x^2 + 3x + 2
(f * g)(x) = f(x) * g(x) = (1 + 1) * (1 + 2) = 2 * 3 = 6
D.) Division of Two Functions
[tex]\mleft(f/g\mright)\mleft(x\mright)=\frac{f(x)}{g(x)}[/tex]In dividing two functions, you divide the output of the functions.
Example: f(x) = x + 1 and g(x) = x + 2
[tex](\frac{f}{g})(x)\text{ = }\frac{f(x)}{g(x)}\text{ = }\frac{x\text{ + 1}}{x\text{ + 2}}[/tex][tex](\frac{f}{g})(1)\text{ = }\frac{f(1)}{g(1)}\text{ = }\frac{1\text{ + 1}}{1\text{ + 2}}\text{ = }\frac{2}{3}[/tex]