f(4b)=4x^2+5x-5
f(x+1)=8x^2+x-3
f(-x)=8x^2+x-3
*I think that the first two use F.O.I.L but i still cant get it
I'm afraid I do not catch your question.
Are you supposed to find f(4b) when f(x)=4x^2+5x-5? Or are you supposed to find f(x) when f(4b)=4x^2+5x-5. The second option does not make sense because the expression f(4b) should not leave any trace of "x" when x=4b.
Please clarify.
x=4b sorry
Would the question then be:
1.
If f(x)=4x^2+5x-5, find f(4b).
In this case,
f(4b)= 4(4b)² + 5(4b) -5
= 4(16b²) + 20b -5
= 64b² + 20b -5
Okay thank you that really makes more since your a lifesaver! Do you know how to do number 2 and 3 that you could walk me through too? I have literally tried them 11 times and it still says they are wrong
2.
First step: write down the function in terms of x:
f(x)=8x^2+x-3
Then substitute x by what is in the parentheses (x+1) in this case. Don't forget the parentheses everywhere you make a substitution:
f(x+1)=8(x+1)² + (x+1) - 3
Expand and collect terms as required:
f(x+1)
=8(x+1)² + (x+1) - 3
=8(x²+2x+1) + x+1 -3
=8x² + 16x + 8 +x+1 -3
=8x² + 17x + 6
Proceed the same way for number 3. Post for checking if necessary. The answer is 8x²-x-3.
To simplify the given expressions, you can indeed apply the FOIL method, but it is important to understand what FOIL represents.
FOIL stands for First, Outer, Inner, Last, which refers to multiplying a sum by another sum.
Now let's break down each expression and apply the FOIL method:
1. f(4b) = 4x^2 + 5x - 5
In this case, you are substituting 4b in place of x. So, rewrite the expression as follows:
f(4b) = 4(4b)^2 + 5(4b) - 5
Expanding the expression:
f(4b) = 4(16b^2) + 20b - 5
Simplifying:
f(4b) = 64b^2 + 20b - 5
2. f(x+1) = 8x^2 + x - 3
In this expression, you have x+1 as the value that replaces x. Here's how to simplify:
f(x+1) = 8(x+1)^2 + (x+1) - 3
Expanding the expression:
f(x+1) = 8(x^2 + 2x + 1) + x + 1 - 3
Applying the distributive property:
f(x+1) = 8x^2 + 16x + 8 + x + 1 - 3
Simplifying:
f(x+1) = 8x^2 + 17x + 6
When expanding expressions using the FOIL method, it is essential to distribute the coefficients (multipliers) to all terms within the parentheses. In both cases, you have a sum inside the parentheses, which requires multiplying each term inside the parentheses by the coefficients outside the parentheses. Then, combine like terms to obtain the simplified expression.
For the third expression, f(-x) = 8x^2 + x - 3, no FOIL method is required since you're simply substituting -x in place of x.