Given:
The functions are:
[tex]f(x)=2x+1[/tex]
[tex]g(x)=x^2[/tex]
To find:
The value of [tex]fg(3)[/tex].
Solution:
We have,
[tex]f(x)=2x+1[/tex]
[tex]g(x)=x^2[/tex]
Substitute [tex]x=3[/tex] in each function.
[tex]f(3)=2(3)+1[/tex]
[tex]f(3)=6+1[/tex]
[tex]f(3)=7[/tex]
And,
[tex]g(3)=(3)^2[/tex]
[tex]g(3)=9[/tex]
We know that, product of two functions is defined as:
[tex]fg(x)=f(x)\times g(x)[/tex]
Using this rule, we get
[tex]fg(3)=f(3)\times g(3)[/tex]
[tex]fg(3)=7\times 9[/tex]
[tex]fg(3)=63[/tex]
Therefore, the value of [tex]fg(3)[/tex] is 63.
