Question

If f(x) = -5x -9 then f^-1(x) = ____

Answer 1

Answer:

$f^{-1}(x)=-\frac{x+9}{5}$;

Step-by-step explanation:

The given linear function is;

$f(x)=-5x-9$

Let $y=-5x-9$;

Interchange $x$ and $y$ to get;

$x=-5y-9$;

Solve for $y$.

$x+9=-5y$

Divide both sides by -5

$\frac{x+9}{-5}=y$;

This implies that;

$f^{-1}(x)=-\frac{x+9}{5}$;

Answer 2

Answer:

f⁻¹(x) =  -(x+9) / 5

Step-by-step explanation:

We have given a function.

f(x) = -5x -9

We have to find inverse of given function.

Let y = f(x)

y = -5x-9

Solving above equation for x, we have

x = -(y+9) / 5

Putting x = f⁻¹(y) in above equation ,we have

f⁻¹(y) =  -(y+9) / 5

Replacing y by x, we have

f⁻¹(x) =  -(x+9) / 5 which is the answer.