Given f, of, x, equals, minus, x, plus, 2f(x)=−x+2, find f, of, minus, 6f(−6)
To find f(-6), plug in -6 for x in the equation 2f(x) = -x + 2:
2f(-6) = -(-6) + 2
2f(-6) = 6 + 2
2f(-6) = 8
Divide both sides by 2 to find f(-6):
f(-6) = 8 / 2
f(-6) = 4
Now, substitute f(-6) = 4 back into the original equation f(x) = -x + 2:
f(x) = -x + 2
f(-6) = -(-6) + 2
f(-6) = 6 + 2
f(-6) = 8
Now, plug f(-6) = 4 and f(-6) = 8 into the given expression f(-6) - 6f(-6):
f(-6) - 6f(-6)
= 4 - 6(8)
= 4 - 48
= -44
Therefore, the value of f(-6) - 6f(-6) is -44.