Question

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

Answer 1

The value of f(-6) is -12.2

Explanation:

Given that the function $f(x)=\frac{100}{-10+e^{-0.1\left(x\right)}}$

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,

$f(-6)=\frac{100}{-10+e^{-0.1\left(-6\right)}}$

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

$f(-6)=\frac{100}{-10+e^{0.1\left(6\right)}}$

Multiplying the numbers, we get,

$f(-6)=\frac{100}{-10+e^{0.6}}$

The value of $e^{0.6}=1.822$

Substituting the value of $e^{0.6}=1.822$ , we get,

$f(-6)=\frac{100}{-10+1.822}$

Subtracting the denominator, we have,

$f(-6)=\frac{100}{-8.178}$

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