Certainly! Let's analyze the function [tex]\( f(x) = -\sqrt{-2x + 4} - 2 \)[/tex] and evaluate it at [tex]\( x = 1 \)[/tex].
1. Substitute [tex]\( x = 1 \)[/tex] into the function [tex]\( f(x) \)[/tex]:
[tex]\[
f(1) = -\sqrt{-2(1) + 4} - 2
\][/tex]
2. Calculate the expression inside the square root:
[tex]\[
-2(1) + 4 = -2 + 4 = 2
\][/tex]
3. Take the square root of the resulting value:
[tex]\[
\sqrt{2}
\][/tex]
4. Include the negative sign in front of the square root:
[tex]\[
-\sqrt{2}
\][/tex]
5. Subtract 2 from the result:
[tex]\[
-\sqrt{2} - 2
\][/tex]
By evaluating this step by step calculation at [tex]\( x = 1 \)[/tex], you obtain the final value:
[tex]\[
f(1) = -\sqrt{2} - 2 \approx -3.414213562373095
\][/tex]
Thus, the value of [tex]\( f(1) \)[/tex] is approximately [tex]\( -3.414213562373095 \)[/tex].
