f -1(x) is said to be the inverse of f(x)
if f(f -1(x)) = f -1(f(x)) = x. It is obtained by interchanging the variables x and y of the function.
Inverse of a function is the reflection of the function about the line y = x.
Inverse of a function does not necessarily always be a function.
y = 3x - 5 is a function where x = 3, 4, 5. y = 3x - 5 = 4, 7, and 10 by substituting the values of x.
Thus, the function is {(3, 4), (4, 7), (5, 10)}.
The inverse of the function is {(4, 3), (7, 4) (10, 5)} by interchanging the first and second co-ordinates.
A. y = 4x + 3
B. y = 4/4x + 7
C. y = 4x +7/4
D. y = x + 7
Correct Answer: C
Step 1: y = 4x - 7/4.
Step 2: Interchange x and y and find y in terms of x.
Step 3: x = 4y - 7/4 [Interchange x and y.]
Step 4: 4x = 4y - 7 [Multiply throughout by 4.]
Step 5: 4x + 7 = 4y [Add 7 to both sides of the equation.]
Step 6: 4x + 7/4 = y
Step 7: The inverse function is y = 4x + 7/4.