Question

given the function f(x) = the quantity of 5x minus 3, divided by 4, which of the below expressions is correct? a. f−1(x) = the quantity of 3 minus 5x, divided by 4 b. f−1(x) = the quantity of 4x plus 3, divided by 5 c. f−1(x) = the quantity of 4x minus 3, divided by 5. d. f−1(x) = the quantity of negative 5x minus 3, divided by 4.

Answer 1

$f(x)= \frac{5x-3}{4} \\ y= \frac{5x-3}{4} \\ 4y=5x-3 \\ 4y+3=5x \\ x= \frac{4y+3}{5} \\ f^{-1} (x)=\frac{4x+3}{5}$

Answer 2

Answer:

Option B. will be the answer.

Step-by-step explanation:

The given function is f(x) = $\frac{5x-3}{4}$

Now we have to find the inverse function $f^{-1}(x)$ of the given function.

We can rewrite the function in the form of an equation.

y = $\frac{5x-3}{4}$

Now flip x by y and y by x.

x = $\frac{5y-3}{4}$

Now solve this equation for the value of y

5y - 3 = 4x

5y = 4x + 3

y = $\frac{(4x+3)}{5}$

Now rewrite the equation in the form of a function which will the inverse of the parent function.

$f^{-1}(x)=\frac{(4x+3)}{5}$

Therefore, Option B. is the answer.