Question

2. Determine the inverse function 𝒇−𝟏(𝒙) for the linear function 𝒚 + 𝟒𝒙 − 𝟓 = 𝟎

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1. Empezamos con la ecuación de la función lineal: y + 4x - 5 = 0

2. Despejamosy : y = -4x + 5

3. Intercambiamosx y y para encontrar la función inversa: x = -4y + 5

4. Despejamosy en términos de x :

x - 5 = -4y

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

y=\frac{-x+5}{4}

Por lo tanto, la función inversa esf^{-1}(x)=\frac{-x+5}{4}

2. Despejamos

3. Intercambiamos

4. Despejamos

Por lo tanto, la función inversa es

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