Question

f(x)={
−(x−4)
2
+6
−2
​

for x

=1
1
1
​

for x=1
1
1
​

​

Find , f, of, 1
Find f(1)

Answer 1

I can’t read the piecewise definition unambiguously from what you typed. Could you confirm the two pieces? It looks like you have one expression for x ≠ 1 and a separate value for x = 1.

If the definition really is
- f(x) = −(x−4)^2 + 6 − 2 for x ≠ 1, and
- f(1) = 11,

then f(1) = 11 (you always use the value given for x = 1, not the other formula).

If instead you meant f(x) = −(x−4)^2 + 4 for x ≠ 1 (since 6−2 = 4), then plugging x = 1 into that formula gives f(1) (from the formula) = −(1−4)^2 + 4 = −9 + 4 = −5. But in a piecewise definition the actual f(1) is whatever the x = 1 branch specifies.

Please confirm the exact piecewise definition if you want a definitive answer.