Answer:
[tex]f^{-1} (x) =[/tex] [tex]\frac{1}{5}(x+3)[/tex]
Step-by-step explanation:
In order to find the inverse of a function we need to follow the given step
We shall do step by step to find the inverse of given function
Step(1) : we write f(x) =y
therefore here y =5x-3
Step(2) Interchanging x and y
x =5y-3
or
5y-3 = x
Step :solving the obtained equation for y
5y = x+3
y = [tex]\frac{1}{5}(x+3)[/tex]
[tex]f^{-1} (x) =[/tex] [tex]\frac{1}{5}(x+3)[/tex]
Answer:
f⁻¹(x) = x+3 / 5
Step-by-step explanation:
We have given a function.
f(x) = 5x-3
We have to find the inverse of given function.
Step 1. Put y = f(x) in given function
y = 5x-3
Step 2. Add 3 to both sides of above equation
y+3 = 5x-3+3
y+3 = 5x
Step 3.Divide by 5 to both sides of above equation
y+3 / 5 = 5x / 5
y+3 / 5 = x
Step 4. Swap sides
x = y+3 / 5
Step 5.Put x = f⁻¹(y) in above equation
f⁻¹(y) = y+3 / 5
Step 6. Replace x with y
f⁻¹(x) = x+3 / 5 is the inverse of f(x) = 5x-3.
