Question

Given the graph of the inverse function below, which of the following is the graph of the original function?

Answer 1

Answer:

A

Step-by-step explanation:

Answer 2

Answer:

The graph of original function is shown below.

Step-by-step explanation:

The graph of the inverse function is given.

From the given graph it is clear that the graph of inverse function is in an exponential function that passes through the points (0,1) and (1,3).

Let the inverse function be

$y=ab^x$

Put x=0 and y=1 in the above equation.

$1=ab^0\Rightarrow a=1$

Put a=1, x=1 and y=3 in the above equation.

$3=(1)b^1\Rightarrow b=3$

So the inverse function is

$y=(3)^x$

Interchange x and y.

$x=(3)^y$

Taking log both the sides.

$logx=log(3)^y$

$logx=ylog(3)$               $[\because logx^a=alog(x)]$

Divide both the sides by log3.

$\frac{logx}{log3}=y$      

$log_3x=y$                     $[\because log_ab=\frac{log_mb}{log_ma}]$

The original function is

$y=log_3x$

The graph of original function is the mirror image of inverse function across the line y=x.

Therefore the graph of original function is shown below.