Question

Consider the functions f(x) = 3x − 2 and g(x) = x2 − 1. What is the value of f[g(5)]?

312

70

168

−1

Answer 1

g(5)=25-1=24, f(24)=3×24-2=72-2=70

Answer 2

The correct option is 2. The value of f[g(5)] is 70.

Explanation:

The given functions are

`f(x)=3x-2`

`g(x)=x^2-1`

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).

`g(5)=5^2-1`

`g(5)=25-1`

`g(5)=24`

The value of g(5) is 24.

`f[g(5)]=f(24)` ..... (1)

Substitute x=24 in the function f(x).

`f(24)=3(24)-2`

`f(24)=72-2`

`f(24)=70` .....(2)

Using (1) and (2) we get

`f[g(5)]=70`

The value of f[g(5)] is 70. Therefore the correct option is 2.