Question

pls see the question​

Answer 1

right answer is option B

Answer 2

Answer:

Option B is correct .i.e., f(x) = 2 + x²

Step-by-step explanation:

Given: g(x) = 1 + √x

           f(g(x)) = 3 + 2√x + x

To find: f(x)

Option A:

Let f(x) = 1 + 2x²

then,

f(g(x)) = 1 + 2(1 + √x)²

          = 1 + 2 (1² + (√x)² + 2√x )

         = 1 + 2( 1 + x + 2√x )

         = 1 + 2 + 2x + 4√x

         = 3 + 2x + 4√x

It not matches with given f(x).

Thus, this option is incorrect.

Option B:

Let f(x) = 2 + x²

then,

f(g(x)) = 2 + (1 + √x)²

          = 2 + 1² + (√x)² + 2√x

         = 2 + 1 + x + 2√x

         = 3 + x + 2√x

It matches with given f(x).

Thus, this option is correct.

Option C:

Let f(x) = 1 + x

then,

f(g(x)) = 1 + (1 + √x)

          = 1 + 1 + √x

         = 2 + √x

It not matches with given f(x).

Thus, this option is incorrect.

Option D:

Let f(x) = 2 + x

then,

f(g(x)) = 2 + (1 + √x)

          = 2 + 1 + √x

         = 3 + √x

It not matches with given f(x).

Thus, this option is incorrect.

Therefore, Option B is correct.