Question

F(x)=4x+1 over 3 , solve for f ^-1 (3)

Answer 1

Answer:

${f}^{ - 1} (3) = 2$

Step-by-step explanation:

$f(x) = \frac{4x + 1}{3}$

To find f-¹(3) we must first find f-¹(x)

To find f-¹(x) equate f(x) to y

That's

$y = \frac{4x + 1}{3}$

Next interchange the terms that's x becomes y and y becomes x

We have

$x = \frac{4y + 1}{3}$

Next make y the subject

Cross multiply

We have

3x = 4y + 1

4y = 3x - 1

Divide both sides by 4

We have

$y = \frac{3x - 1}{4}$

So we have

${f}^{ - 1} (x) = \frac{3 x - 1}{4}$

To find f-¹(3) substitute the value of x that's 3 into f-¹(x)

We have

${f}^{ - 1} (3) = \frac{3(3) - 1}{4} \\ = \frac{9 - 1}{4} \\ = \frac{8}{4}$

We have the final answer as

${f}^{ - 1} (3) = 2$

Hope this helps you