Answer:
Option (d) is correct.
[tex]f[g(3)]=-1[/tex]
Step-by-step explanation:
Given : [tex]f(x)=2x+1[/tex] and [tex]g(x)=x^2-10[/tex]
We have to find the value of [tex]f[g(3)][/tex]
Since, we have to calculate [tex]f[g(3)][/tex]
[tex]f[g(3)][/tex] represents a composition of function f(x) and g(x)
We first find g(3) that is value of g at x = 3
Substitute x = 3 in g(x), we have,
[tex]g(x)=x^2-10[/tex] thus, at x = 3 , we have
[tex]g(3)=3^2-10=9-10=-1[/tex]
now, [tex]f[g(3)][/tex] becomes [tex]f[-1][/tex]
Thus, now we calculate f(x) at x = -1
thus we have,
[tex]f(x)=2x+1[/tex] at x = -1 , we have,
[tex]f(-1)=2(-1)+1=-2+1=-1[/tex]
Thus, [tex]f[g(3)]=-1[/tex]
Option (d) is correct.
