Question

Inverse of an exponential function fill in the chart. If needed, use a calculator and round to one decimal place.

Answer 1

The answers from column to column are :

g, h and s

e, a and b

d, q and r

k, f and c

m, l and n

EXPLANATION :

From the problem, we have the function :

`f(x)=e^x`

The first column is the value of f(x) at given x values.

The second column is also the value of f(x) but written as a point (x, f(x))

The third column is the inverse of the function written as a point (f(x), x)

We will solve this from one column to another column.

That will be :

`\begin{gathered} \text{ when x = 0} \\ f(0)=e^0=1 \\ (x,f(x))=(0,1) \\ (f(x),x)=(1,0) \\ \text{ The answers are g, h and s} \end{gathered}`
`\begin{gathered} \text{ when x = 1} \\ f(1)=e^1\approx2.7 \\ (x,f(x))=(1,2.7) \\ (f(x),x)=(2.7,1) \\ \text{ The answers are e, a and b} \end{gathered}`
`\begin{gathered} \text{ when x = -1} \\ f(-1)=e^(-1)\approx0.4 \\ (x,f(x))=(-1,0.4) \\ (f(x),x)=(0.4,-1) \\ \text{ The answers are d, q and r} \end{gathered}`
`\begin{gathered} \text{ when x = 2} \\ f(2)=e^2\approx7.4 \\ (x,f(x))=(2,7.4) \\ (f(x),x)=(7.4,2) \\ \text{ The answers are k, f and c} \end{gathered}`
`\begin{gathered} \text{ when x = -2} \\ f(-2)=e^(-2)\approx0.1 \\ (x,f(x))=(-2,0.1) \\ (f(x),x)=(0.1,-2) \\ \text{ The answers are m, l and n} \end{gathered}`

g, h and s