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If f (x) = 3x -1, g (x) =x ^(2) + 1 th...

If ` f (x) = 3x -1, g (x) =x ^(2) + 1 ` then `f [g (x)]=`

A

`3x ^(2) + 2`

B

`9x ^(2) -6x +2`

C

`3x ^(2) -2`

D

`9x ^(2) + 6x-2`

Text Solution

AI Generated Solution

The correct Answer is:
To find \( f[g(x)] \), we need to substitute \( g(x) \) into \( f(x) \). 1. **Identify the functions**: - \( f(x) = 3x - 1 \) - \( g(x) = x^2 + 1 \) 2. **Substitute \( g(x) \) into \( f(x) \)**: - We need to find \( f[g(x)] \), which means we will replace \( x \) in \( f(x) \) with \( g(x) \). - So, we have: \[ f[g(x)] = f(x^2 + 1) \] 3. **Apply the function \( f \)**: - Now, substitute \( x^2 + 1 \) into \( f(x) \): \[ f(x^2 + 1) = 3(x^2 + 1) - 1 \] 4. **Simplify the expression**: - Distributing \( 3 \): \[ = 3x^2 + 3 - 1 \] - Combine like terms: \[ = 3x^2 + 2 \] Thus, the final result is: \[ f[g(x)] = 3x^2 + 2 \]
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