Answer:
option (b) is correct
inverse of function [tex]f(x)=\frac{x+3}{4}[/tex] is 4x+3
Step-by-step explanation:
Given function [tex]f(x)=\frac{x+3}{4}[/tex]
We have to find the inverse of given function.
Let f(x) = y then taking inverse both sides, we get
[tex]f^{-1}(y)=f^{-1}(f(x))\\\\\ f^{-1}(y)=x[/tex]
Substitute , x and f(x) in given equation, we get,
[tex]f(x)=\frac{x+3}{4} \Rightarrow \frac{(f^{-1}(y))+3}{4}[/tex]
Now solve for [tex](f^{-1}(y))[/tex] , we get,
[tex](f^{-1}(y))+3=4y[/tex]
[tex](f^{-1}(y))=4y-3[/tex]
Thus, inverse of function [tex]f(x)=\frac{x+3}{4}[/tex] is 4x+3
Thus, option (b) is correct.
Answer:
Choice b is correct.
The inverse of function f(x)=x+3/4 is 4x-3
Step-by-step explanation:
Given function is:
f(x)=x+3 / 4
We have to find the inverse of f(x)
Put f(x)=y in above equation
y = x+3 / 4
We have to separate x from above equation.
Multiplying 4 on both sides of above equation,we have
4y=(x+3)
Adding -3 to both sides of above equation,we have
4y-3=x+3-3
x=4y-3
Replacing y to x and x to f⁻¹(x) we have
f⁻¹(x)=4x-3
This is our required result.
The inverse of the function f(x)=x+3/4 is 4x-3
