Question

Arithmetic and Functions

Answer 1

Choice D is correct answer.

Explanation:

From question statement, we observe that

h(x) = (f*g)(x) and h(x) = 4(x+1)²

We have to find possibilities for f(x) and g(x).

Comparing above equation,we get

4(x+1)² = f(g(x))

From possibilities,

let g(x) = x+1 and f(x) = 4x²

h(x) = f(g(x)) = f(x+1)

h(x) = 4(x+1)² which is the answer.

Answer 2

Option D is correct.

`f(x) = 4x^2`

`g(x) = x+1`

Explanation:

As per the statement:

If
`h(x) = (fog)(x)` and
`h(x) = 4(x+1)^2`

Find: f(x) and g(x).

`h(x) = (f(g(x))`

`4(x+1)^2=f(g(x))`

From the options

let
`g(x) = x+1` and
`f(x) = 4x^2`

then;

`f(g(x)) = f(x+1)`

Replace x with x+1 in f(x) we have;

`f(g(x)) = f(x+1) = 4(x+1)^2`

Therefore, one possibility for f(x) and g(x) is:

`f(x) = 4x^2`

`g(x) = x+1`