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Lerok [7]
2 years ago
14

Consider the following function: f(x)=-3/4x+9

Mathematics
2 answers:
miv72 [106K]2 years ago
8 0

Answer:

f^{-1}(x) =  ( \frac{4y - 36}{-3} )

Step-by-step explanation:

f(x)=-3/4x+9

let f(x) be y .......................to find inverse we have making x the subject.

y = -3/4x+9

y - 9 = -3/4 x

-3x = 4y - 36

x = (4y - 36)/-3

so, f^{-1}(x) =  ( \frac{4y - 36}{-3} )

rusak2 [61]2 years ago
8 0
  • Let y=f(x)

\\ \tt\hookrightarrow y=\dfrac{-3}{4}x+9

\\ \tt\hookrightarrow y-9=\dfrac{-3x}{4}

\\ \tt\hookrightarrow -3x=4y-36

\\ \tt\hookrightarrow x=\dfrac{-4}{3}y+12

Now

\\ \tt\hookrightarrow f^{-1}x=\dfrac{-4}{3}x+12

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GalinKa [24]

Answer:

\large \boxed{\sf \bf \ \ f(x)=(x-4i)(x+4i)(x+3)(x-5) \ \ }

Step-by-step explanation:

Hello, the Conjugate Roots Theorem states that if a complex number is a zero of real polynomial its conjugate is a zero too. It means that (x-4i)(x+4i) are factors of f(x).

\text{Meaning that } (x-4i)(x+4i) =x^2-(4i)^2=x^2+16 \text{ is a factor of f(x).}

The coefficient of the leading term is 1 and the constant term is -240 = 16 * (-15), so we a re looking for a real number such that.

f(x)=x^4-2x^3+x^2-32x-240\\\\ =(x^2+16)(x^2+ax-15)\\\\ =x^4+ax^3-15x^2+16x^2+16ax-240

We identify the coefficients for the like terms, it comes

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\\f(x)=(x^2+16)(x^2-2x-15)

The sum of the zeroes is 2=5-3 and their product is -15=-3*5, so we can factorise by (x-5)(x+3), which gives.

f(x)=(x^2+16)(x^2-2x-15)\\\\=(x^2+16)(x^2+3x-5x-15)\\\\=(x^2+16)(x(x+3)-5(x+3))\\\\=\boxed{(x^2+16)(x+3)(x-5)}

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f(x)=\boxed{(x-4i)(x+4i)(x+3)(x-5)}

Hope this helps.

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How to write 0.000298 in scientific notation? 0.000298 written as scientific notation is 2.98 × 10-4.

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