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Question

Consider f:RR given by f(x)=4x+3. Show that f is invertible. Find the inverse of f

A
y=(x+3)4
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B
y=(x3)4
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C
y=(x3)4
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D
y=(x3)4
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Solution

The correct option is B y=(x3)4
A function is a one-to-one function if and only if each second element corresponds to one and only one first element. (each x and y value is used only once)
Use the horizontal line test to determine if a function is a one-to-one function.
If ANY horizontal line intersects your original function in ONLY ONE location, your function will be a one-to-one function and its inverse will also be a function.
Now,
f(x)=4x+3 is one-to-one function , Therefore it has inverse function
Now express the given function in following way
x=4y+3 , Now express y in terms of x, y will be inverse
y=(x3)4 is f1

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