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gulaghasi [49]
3 years ago
14

What is the inverse of f(x) = -5x-4

Mathematics
2 answers:
elena55 [62]3 years ago
8 0

Answer:

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

Step-by-step explanation:

The question has provided an expression for the function f(x) and is asking for its inverse, f^{-1}(x).

Based on the definition of inverse functions,

f(f^{-1}(x)) = x.

Let y = f^{-1}(x).

f(y) = x.

-5 y - 4= x.

Solve this equation for f^{-1}(x) = y:

-5y = x +4.

\displaystyle y = (-\frac{1}{5})\cdot (x + 4) = -\frac{x}{5} -\frac{4}{5}.

However, f^{-1}(x)=y As a result,

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

madreJ [45]3 years ago
6 0

Answer:

\large\boxed{f^{-1}(x)=-\dfrac{x+4}{5}}

Step-by-step explanation:

f(x)=-5x-4\to y=-5x-4\\\\\text{Exchange x to y and vice versa:}\\\\x=-5y-4\\\\\text{Solve for}\ y:\\\\-5y-4=x\qquad\text{add 4 to both sides}\\\\-5y=x+4\qquad\text{divide both sides by (-5)}\\\\\dfrac{-5y}{-5}=\dfrac{x+4}{-5}\\\\y=-\dfrac{x+4}{5}

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