Question 886712
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(x)=5x^2+5x-7}}} Start with the given function.


{{{f(k-1)=5(k-1)^2+5(k-1)-7}}} Replace EVERY x with k-1. 


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


{{{f(k-1)=5(k-1)(k-1)+5(k-1)-7}}} Taking advantage of the fact that {{{x^2 = x*x}}}


{{{f(k-1)=5(k^2 - 2k + 1)+5(k-1)-7}}} FOIL/expand


{{{f(k-1)=5(k^2) + 5(- 2k) + 5(1)+5(k) + 5(-1)-7}}} Distribute


{{{f(k-1)=5k^2 -10k + 5+5k -5-7}}} Multiply


{{{f(k-1)=5k^2+(-10k+5k) + (5 -5-7)}}} Group like terms.


{{{f(k-1)=5k^2-5k -7}}} Combine like terms.




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


So the final answer is {{{f(k-1)=5k^2-5k -7}}}