Question

Question 25?Find the inverse of the given function. Graph both functions on the same set of axes and show the line Y=x as a dotted line on the graph?

Answer 1

Question 25.

Given the function:

f(x) = 2x + 1

Let's find the inverse of the function.'

Rewrite f(x) for y:

y = 2x + 1

Interchange the variables:

x = 2y + 1

Now, solve the equation for y:

x =2y + 1

Subtract 1 from both sides:

x - 1 = 2y + 1 - 1

x - 1 =2y

Divide all terms by 2:

`\begin{gathered} (x)/(2)-(1)/(2)=(2y)/(2) \\ \\ (1)/(2)x-(1)/(2)=y \\ \\ y=(1)/(2)^{}x-(1)/(2) \end{gathered}`

The inverse of the function is:

`f^(-1)(x)=(1)/(2)x-(1)/(2)`

Let's graph both the inverse and parent functions using two lines each.

For the paent function

y = 2x + 1

When x = 1:

y = 2(1) + 1

y = 3

When x = 2:

y = 2(2) + 1

y = 5

We have the points:

(1, 3) and (2, 5)

For the inverse function:

When x = 1

`\begin{gathered} y=(1)/(2)(1)-(1)/(2) \\ \\ y=0 \end{gathered}`

When x = 2:

`\begin{gathered} y=(1)/(2)(2)-(1)/(2) \\ \\ y=(1)/(2)=0.5 \end{gathered}`

We have the points:

(1, 0) and (2, 0.5)

The graph is attached below

The red line represents the parent function.

The blue line represents the inverse.

The green dotted line represents the line (y = x).