Given:
[tex]f(x)=3(x-5)+8[/tex]
To find:
The inverse [tex]f^{-1}(x)[/tex] of given function
Solution:
We have,
[tex]f(x)=3(x-5)+8[/tex]
[tex]f(x)=3x-15+8[/tex]
[tex]f(x)=3x-7[/tex]
Put f(x)=y.
[tex]y=3x-7[/tex]
Interchange x and y.
[tex]x=3y-7[/tex]
Isolate y on one side.
[tex]x+7=3y[/tex]
[tex]\dfrac{x+7}{3}=y[/tex]
[tex]y=\dfrac{x+7}{3}[/tex]
Put [tex]y=f^{-1}(x)[/tex].
[tex]f^{-1}(x)=\dfrac{x+7}{3}[/tex]
Therefore, the required inverse function is [tex]f^{-1}(x)=\dfrac{x+7}{3}[/tex].
The inverse function of f(x) is [tex]f^{-1}(x) = 5 + \frac{x - 8}{3}[/tex]
The function is given as:
[tex]f(x) = 3(x - 5) + 8[/tex]
Replace f(x) with y
[tex]y = 3(x - 5) + 8[/tex]
Swap the positions of x and y
[tex]x = 3(y - 5) + 8[/tex]
Subtract 8 from both sides
[tex]x - 8= 3(y - 5)[/tex]
Divide both sides by 3
[tex]\frac{x - 8}{3} = y - 5[/tex]
Add 5 to both sides
[tex]5 + \frac{x - 8}{3} = y[/tex]
Rewrite as:
[tex]y = 5 + \frac{x - 8}{3}[/tex]
Replace y with the inverse function
[tex]f^{-1}(x) = 5 + \frac{x - 8}{3}[/tex]
Hence, the inverse function of f(x) is [tex]f^{-1}(x) = 5 + \frac{x - 8}{3}[/tex]
Read more about inverse functions at:
https://brainly.com/question/14391067
