Given:
The function is:
[tex]f(x)=-2x+5[/tex]
To find:
The inverse of the given function, then draw the graphs of function and its inverse.
Solution:
We have,
[tex]f(x)=-2x+5[/tex]
Step 1: Substitute [tex]f(x)=y[/tex] .
[tex]y=-2x+5[/tex]
Step 2: Interchange x and y.
[tex]x=-2y+5[/tex]
Step 3: Isolate variable y.
[tex]2y=5-x[/tex]
[tex]y=\dfrac{5-x}{2}[/tex]
Step 4: Substitute [tex]y=f^{-1}(x)[/tex].
[tex]f^{-1}(x)=\dfrac{5-x}{2}[/tex]
Therefore, the inverse of the given function is [tex]f^{-1}(x)=\dfrac{5-x}{2}[/tex] and the graphs of these functions are shown below.
Note: The inverse function is [tex]f^{-1}(x)=g(x)[/tex].
