SOLUTION: Please help me solve this problem: Find f(k-1)when f(x)=5x^2+5x-7.

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Question 886712: Please help me solve this problem: Find f(k-1)when f(x)=5x^2+5x-7.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
The idea is this: Everywhere you see an 'x', you replace it with k-1. This is what it means to plug in x = k-1



f%28x%29=5x%5E2%2B5x-7 Start with the given function.

f%28k-1%29=5%28k-1%29%5E2%2B5%28k-1%29-7 Replace EVERY x with k-1.

** Take special note of the parenthesis on the right side **

f%28k-1%29=5%28k-1%29%28k-1%29%2B5%28k-1%29-7 Taking advantage of the fact that x%5E2+=+x%2Ax

f%28k-1%29=5%28k%5E2+-+2k+%2B+1%29%2B5%28k-1%29-7 FOIL/expand

f%28k-1%29=5%28k%5E2%29+%2B+5%28-+2k%29+%2B+5%281%29%2B5%28k%29+%2B+5%28-1%29-7 Distribute

f%28k-1%29=5k%5E2+-10k+%2B+5%2B5k+-5-7 Multiply

f%28k-1%29=5k%5E2%2B%28-10k%2B5k%29+%2B+%285+-5-7%29 Group like terms.

f%28k-1%29=5k%5E2-5k+-7 Combine like terms.



It's a lot of work, but hopefully it makes sense.

So the final answer is f%28k-1%29=5k%5E2-5k+-7