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