Given f, left bracket, x, right bracket, equals, minus, x, squared, minus, 5f(x)=−x

Question

2
−5, find f, left bracket, minus, 1, right bracketf(−1)

Answer 1

To find f(-1), we substitute -1 into the equation:

f(x) = -x^2 - 5f(x)

f(-1) = -(-1)^2 - 5f(-1)

Simplifying this, we have:

f(-1) = -1 - 5f(-1)

Now, let's solve the equation for f(-1):

6f(-1) = -1

Dividing both sides by 6:

f(-1) = -1/6