Answer:
[tex]\text{f}^{-1}(x)=\dfrac{x-15}{12}[/tex]
Step-by-step explanation:
[tex]\text{f}^{-1}(x)[/tex] is the notation for the inverse of a function.
The inverse of a function is a reflection in the line y = x.
Given function:
[tex]\text{f}(x)=15+12x[/tex]
To find the inverse of the given function:
Step 1
Replace f(x) with y to get an equation for y in terms of x:
[tex]\implies y=15+12x[/tex]
Step 2
Rearrange the equation to make x the subject:
[tex]\implies y-15=15+12x-15[/tex]
[tex]\implies y-15=12x[/tex]
[tex]\implies \dfrac{y-15}{12}=\dfrac{12x}{12}[/tex]
[tex]\implies x=\dfrac{y-15}{12}[/tex]
Step 3
Replace x with [tex]\text{f}^{-1}(x)[/tex] and y with x → this is the inverse function:
[tex]\implies \text{f}^{-1}(x)=\dfrac{x-15}{12}[/tex]
Step 4 (if necessary)
The domain of the function is the range of the inverse function.
The range of the function is the domain of the inverse function.
Therefore, as the domain and range of the given function are unrestricted, so too are the domain and the range of the inverse function:
Learn more about inverse functions here:
https://brainly.com/question/16071767
[tex]\\ \rm\leadsto y=15+12x[/tex]
Interchange x and y
[tex]\\ \rm\leadsto x=15+12y[/tex]
Solve for y
[tex]\\ \rm\leadsto 12y=x-15[/tex]
[tex]\\ \rm\leadsto y=\dfrac{x-15}{12}[/tex]
That's the inverse
