What is the inverse of f(x)=4x+3 ?

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4 Answers
Dec 10, 2017

f^-1 (x) = 1/4 x - 3/4

Explanation:

When finding the inverse:
Swap the x with f^-1 (x) and swap f(x) with x:

=> x = 4f^-1 (x) + 3

=> x -3 = 4f^-1 (x)

=> (x-3)/4 = f^-1 (x)

=> 1/4 x -3/4 = f^-1(x)

Dec 10, 2017

f^(-1) x= 1/4 x -3/4

Explanation:

Let y=f(x)=4x+3. Now interchange x and y and then solve for y. Accordingly, x =4y+3
Therefore 4y= x-3
which gives y=f^(-1) x=1/4 (x-3)= 1/4 x -3/4

Dec 10, 2017

It's the first answer.

Explanation:

To find the inverse of a function, invert x and y.
Then, isolate y and you have it.

So, our initial function is f(x)=4x+3.
We can rewrite it as y=4x+3,

Then, invert x and y:
x=4y+3

And now, isolate y:
x-3=4y
y=1/4(x-3)
y=1/4x-3/4

And finally, replace y with the inverse function notation:
f^-1=1/4x-3/4

So, it's the first answer.

Dec 10, 2017

f^-1(x)=1/4x-3/4

Explanation:

Consider this as a function machine, where we put x into the machine, and get f(x) out.

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If we have this, what do we need to do to f(x) to get x back out?

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so if f(x)=4x+3 then
f^-1(x)=(x-3)/4
f^-1(x)=1/4x-3/4