Question
Which of the following functions is the inverse of $f(x)=-4 x+3$

Select all that apply:
$g(x)=-\frac{x}{4}+\frac{4}{3}$
$g(x)=-\frac{x}{4}+\frac{3}{4}$
$g(x)=\frac{x}{4}-\frac{3}{4}$
$g(x)=-\frac{x}{3}+\frac{3}{4}$

Answer

Expert–verified

Hide Steps

Answer

$\boxed{\text{None of the given options is the inverse of } f(x)=-4 x+3}$

Steps

Step 1 ：The given function is $f(x)=-4 x+3$.

Step 2 ：The inverse of a function is obtained by swapping the x and y (or f(x)) values. This means we replace f(x) with x and solve for y.

Step 3 ：Let's replace f(x) with x in the given function, we get $x=-4y+3$.

Step 4 ：Solving this equation for y, we get the inverse function as $y=\frac{3}{4}-\frac{x}{4}$.

Step 5 ：Comparing this function with the given options, we find that none of the options match the inverse function.

Step 6 ：$\boxed{\text{None of the given options is the inverse of } f(x)=-4 x+3}$