Question

pls help; use inverse operations to write the inverse of F(x)= x/4 - 5

Answer 1

Answer:

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

Step-by-step explanation:

So we have the function:

$f(x)=\frac{x}{4}-5$

To find the inverse of a function, switch f(x) and x, change f(x) to f⁻¹(x), and solve for it. Thus:

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

Add 5 to both sides:

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

Multiply both sides by 4:

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

And we're done!

Hope this helps!

Answer 2

Answer:

$\huge \boxed{F^{-1}(x)=4(x+5)}$

$\rule[225]{225}{2}$

Step-by-step explanation:

$\displaystyle F(x)= \frac{x}{4} - 5$

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

Switching variables,

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

Solving for y,

$\displaystyle x+5= \frac{y}{4}$

$4(x+5)=y$

$\rule[225]{225}{2}$