Question

operations on functions. Write your own definition and steps on performing
each functions operation. You may give your own example to better illustrate
your point.
Division
Composition
Multiplication
Subtraction
Addition pleaseew help meee​

Answer 1

GIVEN :

Operations on functions. Write your own definition and steps on performing

each functions operation. Give your own example

i) Division

ii) Composition

iii) Multiplication

iv) Subtraction

v) Addition ​

TO FIND :

Operations on functions. Write your own definition and steps on performing

each functions operation.

i) Division

ii) Composition

iii) Multiplication

iv) Subtraction

v) Addition ​

SOLUTION :

Let f(x) and g(x) be any two functions and is defined by $f(x)=x^2+1$ and g(x)=x

Now we can do the operations on functions :

i) Division

$\frac{f}{g}(x)=\frac{f(x)}{g(x)}$

Put the values of functions in the above equation.

⇒ $\frac{f}{g}(x)=\frac{x^2+1}{x}$

ii) Composition

$(f\circ g)(x)=f(g(x))$

Put the values of functions in the above equation

$(f\circ g)(x)=f(x)$

$=x^2+1$

⇒ $(f\circ g)(x)=x^2+1$

iii) Multiplication

(f.g)(x)=f(x).g(x)

Put the values of functions in the above equation

$(f.g)(x)=(x^2+1)(x)$

$=x^3+x$

⇒ $(f.g)(x)=x^3+x$

iv) Subtraction

(f-g)(x)=f(x)-g(x)

Put the values of functions in the above equation

⇒ $(f-g)(x)=x^2+1-x$

v) Addition

(f+g)(x)=f(x)+g(x)

Put the values of functions in the above equation

⇒ $(f+g)(x)=x^2+1+x$