Question

Let f(x)= 100 / −10+ e^ −0.1x . What is f(−6) ?

Enter your answer, rounded to the nearest tenth, in the box.

Answer 1

The value of f(-6) is -12.2

Step-by-step explanation:

Given that the function
`f(x)=(100)/(-10+e^(-0.1\left(x\right)))`

We need to determine the value of f(-6)

The value of f(-6) can be determined by substituting the value for
`x=-6` in the function and simplify the function.

Hence, let us substitute
`x=-6` in the function, we get,

`f(-6)=(100)/(-10+e^(-0.1\left(-6\right)))`

Let us apply the rule
`-\left(-a\right)=a` , we get,

`f(-6)=(100)/(-10+e^(0.1\left(6\right)))`

Multiplying the numbers, we get,

`f(-6)=(100)/(-10+e^(0.6))`

The value of
`e^(0.6)=1.822`

Substituting the value of
`e^(0.6)=1.822` , we get,

`f(-6)=(100)/(-10+1.822)`

Subtracting the denominator, we have,

`f(-6)=(100)/(-8.178)`

Dividing, we have,

`f(-6)=-12.228`

Rounding off to the nearest tenth, we have,

`f(-6)=-12.2`

Thus, the value of f(-6) is -12.2