Question

If ,f(x)=1/4x+3 what is the equation for f–1(x)?


f–1(x) = 4x - 3


f–1(x) = 4(x - 3)


f–1(x) = 4(x + 3)


f–1(x) = 4x + 3

Answer 1

Answer:

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

Step-by-step explanation:

We would like to find the inverse of the following function .

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

Step 1 : Replace $f(x)$ with $y$ . We have

$\longrightarrow y =\dfrac{1}{4}x +3$

Step 2 : Interchange x and y :-

$\longrightarrow x = \dfrac{1}{4}y + 3$

Step 3 : Solve for y :-

$\longrightarrow x - 3 =\dfrac{1}{4}y$

Multiply both sides by 4,

$\longrightarrow 4(x-3) = y$

Step 4 : Replace y with f-¹(x) :-

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

Interchange the sides ,

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

And we are done !