Question

If f(x) = " align="absmiddle" class="latex-formula">, what is the equation for f–1(x)?
f–1(x) = 4(x + 3)

f–1(x) = 4x - 3

f–1(x) = 4(x - 3)

f–1(x) = 4x + 3

Answer 1

Answer:

option (b) is correct

inverse of function  $f(x)=\frac{x+3}{4}$ is 4x+3

Step-by-step explanation:

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

We have to find the inverse of given function.

Let f(x) = y then taking inverse both sides, we get

$f^{-1}(y)=f^{-1}(f(x))\\\\\ f^{-1}(y)=x$

Substitute , x  and f(x) in given equation, we get,

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

Now solve for $(f^{-1}(y))$ , we get,

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

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

Thus, inverse of function  $f(x)=\frac{x+3}{4}$ is 4x+3

Thus, option (b) is correct.

Answer 2

Answer:

Choice b is correct.

The inverse of function f(x)=x+3/4 is 4x-3

Step-by-step explanation:

Given function is:  

f(x)=x+3 / 4  

We have to find the inverse of f(x)

Put f(x)=y in above equation

y = x+3 / 4

We have to separate x from above equation.

Multiplying 4 on both sides of above equation,we have

4y=(x+3)

Adding -3 to both sides of above equation,we have

4y-3=x+3-3

x=4y-3

Replacing y to x and x to f⁻¹(x) we have

f⁻¹(x)=4x-3

This is our required result.

The inverse of the function f(x)=x+3/4 is 4x-3