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

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4 Answers
Dec 10, 2017

f1(x)=14x34

Explanation:

When finding the inverse:
Swap the x with f1(x) and swap f(x) with x:

x=4f1(x)+3

x3=4f1(x)

x34=f1(x)

14x34=f1(x)

Dec 10, 2017

f1x=14x34

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=f1x=14 (x-3)= 14x34

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:
x3=4y
y=14(x3)
y=14x34

And finally, replace y with the inverse function notation:
f1=14x34

So, it's the first answer.

Dec 10, 2017

f1(x)=14x34

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
f1(x)=x34
f1(x)=14x34