Verified Answer :
YES
We can work out the inverse using Algebra. Put "y" for "f(x)" and solve for x:
The function: f(x)=2x+3Put "y" for "f(x)": y=2x+3
Subtract 3 from both sides:
y-3=2x
Divide both sides by 2:
(y-3)/2=x
Swap sides: x=(y-3)/2
Solution (put "f-1(y)" for "x") : f-1(y)=(y-3)/2
Answer:
The given statement is false.
Step-by-step explanation:
Given : For any function, \(x=f^{-1}(y)\) then \(y=f(x)\)
To find : The above statement is true or false?
Solution :
In the above statement the condition \(x=f^{-1}(y)\) then \(y=f(x)\) is valid for some function not for all.
Which means the statement is not true.
Taking a contrary example,
A trigonometric function
The function\(y=\sin x\) is one-one and onto in the domain\([-\frac{\pi}{2},\frac{\pi}{2}]\)
Thus, its inverse exists in \([-\frac{\pi}{2},\frac{\pi}{2}]\)
i.e., \(\text{In }[-\frac{\pi}{2},\frac{\pi}{2}],\ y=\sin x \Rightarrow\ x=\sin^{-1}(y).\)
It depends on the domain for the given statement to be true.
Therefore, The given statement is false.