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If f:R to R, f(x) =x^(2)+2x -3 and g:R t...

If `f:R to R, f(x) =x^(2)+2x -3` and `g:R to R, g(x) =3x-4` then the value of fog(x) is :

A

`3x^(2)+6x-13`

B

`9x^(2)-18x+5`

C

`(3x-4)^(2) +2x-3`

D

`x^(2)+1`

Text Solution

AI Generated Solution

The correct Answer is:
To find the value of \( f(g(x)) \), we will follow these steps: 1. **Identify the functions**: - \( f(x) = x^2 + 2x - 3 \) - \( g(x) = 3x - 4 \) 2. **Substitute \( g(x) \) into \( f(x) \)**: - We need to find \( f(g(x)) \), which means we will replace \( x \) in \( f(x) \) with \( g(x) \). - Therefore, \( f(g(x)) = f(3x - 4) \). 3. **Write the expression for \( f(g(x)) \)**: - Substitute \( g(x) \) into the function \( f \): \[ f(g(x)) = (3x - 4)^2 + 2(3x - 4) - 3 \] 4. **Expand \( (3x - 4)^2 \)**: - Using the formula \( (a-b)^2 = a^2 - 2ab + b^2 \): \[ (3x - 4)^2 = 9x^2 - 24x + 16 \] 5. **Calculate \( 2(3x - 4) \)**: - Distributing the 2: \[ 2(3x - 4) = 6x - 8 \] 6. **Combine all parts**: - Now, substitute back into the expression for \( f(g(x)) \): \[ f(g(x)) = (9x^2 - 24x + 16) + (6x - 8) - 3 \] 7. **Simplify the expression**: - Combine like terms: \[ f(g(x)) = 9x^2 - 24x + 6x + 16 - 8 - 3 \] - This simplifies to: \[ f(g(x)) = 9x^2 - 18x + 5 \] Thus, the final answer is: \[ f(g(x)) = 9x^2 - 18x + 5 \]
To find the value of \( f(g(x)) \), we will follow these steps: 1. **Identify the functions**: - \( f(x) = x^2 + 2x - 3 \) - \( g(x) = 3x - 4 \) 2. **Substitute \( g(x) \) into \( f(x) \)**: - We need to find \( f(g(x)) \), which means we will replace \( x \) in \( f(x) \) with \( g(x) \). ...
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