Answer:
The correct option is 2. The value of f[g(5)] is 70.
Step-by-step explanation:
The given functions are
[tex]f(x)=3x-2[/tex]
[tex]g(x)=x^2-1[/tex]
We need to find the value of f[g(5)].
First of all find the value of g(5). Substitute x=5 in the function g(x).
[tex]g(5)=5^2-1[/tex]
[tex]g(5)=25-1[/tex]
[tex]g(5)=24[/tex]
The value of g(5) is 24.
[tex]f[g(5)]=f(24)[/tex] ..... (1)
Substitute x=24 in the function f(x).
[tex]f(24)=3(24)-2[/tex]
[tex]f(24)=72-2[/tex]
[tex]f(24)=70[/tex] .....(2)
Using (1) and (2) we get
[tex]f[g(5)]=70[/tex]
The value of f[g(5)] is 70. Therefore the correct option is 2.
