The value of f(-6) is -12.2
Explanation:
Given that the function [tex]f(x)=\frac{100}{-10+e^{-0.1\left(x\right)}}[/tex]
We need to determine the value of f(-6)
The value of f(-6) can be determined by substituting the value for [tex]x=-6[/tex] in the function and simplify the function.
Hence, let us substitute [tex]x=-6[/tex] in the function, we get,
[tex]f(-6)=\frac{100}{-10+e^{-0.1\left(-6\right)}}[/tex]
Let us apply the rule [tex]-\left(-a\right)=a[/tex] , we get,
[tex]f(-6)=\frac{100}{-10+e^{0.1\left(6\right)}}[/tex]
Multiplying the numbers, we get,
[tex]f(-6)=\frac{100}{-10+e^{0.6}}[/tex]
The value of [tex]e^{0.6}=1.822[/tex]
Substituting the value of [tex]e^{0.6}=1.822[/tex] , we get,
[tex]f(-6)=\frac{100}{-10+1.822}[/tex]
Subtracting the denominator, we have,
[tex]f(-6)=\frac{100}{-8.178}[/tex]
Dividing, we have,
[tex]f(-6)=-12.228[/tex]
Rounding off to the nearest tenth, we have,
[tex]f(-6)=-12.2[/tex]
Thus, the value of f(-6) is -12.2
