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If f(x)=x^2+2x+1, then: f(x-1)-=...

If `f(x)=x^2+2x+1`, then: `f(x-1)-=`

A

`x^2-2x-1`

B

`x^2`

C

`x^2-2x+1`

D

none of these.

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem, we need to find \( f(x-1) \) given that \( f(x) = x^2 + 2x + 1 \). ### Step-by-Step Solution: 1. **Substitute \( x-1 \) into the function \( f(x) \)**: \[ f(x-1) = (x-1)^2 + 2(x-1) + 1 \] 2. **Expand \( (x-1)^2 \)**: \[ (x-1)^2 = x^2 - 2x + 1 \] 3. **Expand \( 2(x-1) \)**: \[ 2(x-1) = 2x - 2 \] 4. **Combine all parts together**: \[ f(x-1) = (x^2 - 2x + 1) + (2x - 2) + 1 \] 5. **Simplify the expression**: - Combine like terms: \[ f(x-1) = x^2 - 2x + 1 + 2x - 2 + 1 \] - The \( -2x \) and \( 2x \) cancel each other out: \[ f(x-1) = x^2 + (1 - 2 + 1) \] - Simplifying the constants: \[ 1 - 2 + 1 = 0 \] - Therefore: \[ f(x-1) = x^2 + 0 = x^2 \] ### Final Answer: \[ f(x-1) = x^2 \] ---
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