Answer :
To evaluate the function [tex]\( f(x) = -6^{5x+6} \)[/tex] at [tex]\( x = -1 \)[/tex], we need to substitute [tex]\(-1\)[/tex] into the expression in place of [tex]\( x \)[/tex].
Here's how we can do it step-by-step:
1. Substitute the value: Replace [tex]\( x \)[/tex] with [tex]\(-1\)[/tex] in the function.
[tex]\[
f(-1) = -6^{5(-1) + 6}
\][/tex]
2. Simplify the exponent: Calculate the value inside the exponent.
[tex]\[
5(-1) + 6 = -5 + 6 = 1
\][/tex]
3. Evaluate the expression: Substitute the exponent back into the function.
[tex]\[
f(-1) = -6^1
\][/tex]
4. Simplify further: Since [tex]\( 6^1 \)[/tex] is simply [tex]\( 6 \)[/tex], we have:
[tex]\[
f(-1) = -6
\][/tex]
Thus, the evaluated result of the function [tex]\( f(x) \)[/tex] at [tex]\( x = -1 \)[/tex] is [tex]\(-6\)[/tex].
Here's how we can do it step-by-step:
1. Substitute the value: Replace [tex]\( x \)[/tex] with [tex]\(-1\)[/tex] in the function.
[tex]\[
f(-1) = -6^{5(-1) + 6}
\][/tex]
2. Simplify the exponent: Calculate the value inside the exponent.
[tex]\[
5(-1) + 6 = -5 + 6 = 1
\][/tex]
3. Evaluate the expression: Substitute the exponent back into the function.
[tex]\[
f(-1) = -6^1
\][/tex]
4. Simplify further: Since [tex]\( 6^1 \)[/tex] is simply [tex]\( 6 \)[/tex], we have:
[tex]\[
f(-1) = -6
\][/tex]
Thus, the evaluated result of the function [tex]\( f(x) \)[/tex] at [tex]\( x = -1 \)[/tex] is [tex]\(-6\)[/tex].
