Answer:
-1
f (x) = -3(x + 5)
Step-by-step explanation:
1) in f(x) = 1/3x-5, replace f(x)= with y= as follows: y = (1/3)x - 5
2) interchange x and y, obtaining: x = (1/3)y - 5
3) solve this result for y: (1/3)y = -x - 5, or -(x + 5). Next, multiply both sides by 3 to eliminate the fraction (1/3): y = -3(x + 5)
4) replace y with the symbol for "inverse of f(x);
-1
f (x) = -3(x + 5)
The inverse of the function is [tex]f(x)^{-1}[/tex]=3x+15.
The given function is f(x) = 1/3x-5.
We need to find the inverse of the function.
In a function, "f(x)" or "y" represents the output and "x" represents the input. To find the inverse of a function, you switch the inputs and the outputs.
Now, f(x) = [tex]\frac{1}{3}[/tex]x-5 ⇒y=[tex]\frac{1}{3}[/tex]x-5
⇒x=[tex]\frac{1}{3}[/tex]y-5
⇒3x=y-15
⇒y=3x+15
⇒[tex]f(x)^{-1}[/tex]=3x+15
Therefore, the inverse of the function is [tex]f(x)^{-1}[/tex]=3x+15.
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