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Ivenika [448]
2 years ago
14

F(x)=ax+b/2 then f^-1 (x-1) =2x-5/2 find a and b​

Mathematics
1 answer:
krok68 [10]2 years ago
8 0

From the given inverse function, we have

f^{-1}(x-1) = 2x - \dfrac52 \\\\ \implies f^{-1}(x) = f^{-1}((x+1)-1) = 2(x+1) - \dfrac52 = 2x-\dfrac12

By definition of inverse function,

f\left(f^{-1}(x)\right) = x

so that

f\left(2x-\dfrac12\right) = x

a\left(2x-\dfrac12\right) + \dfrac b2 = x

2ax - \dfrac a2 + \dfrac b2 = x

\implies\begin{cases}2a=1 \\\\ -\dfrac a2+\dfrac b2 = 0\end{cases}

\implies \boxed{a=\dfrac12}

\implies \dfrac b2 = \dfrac a2 \implies \boxed{b=\dfrac12}

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Answer:

<u><em>(–20)</em></u> for the resulting output voltages

Step-by-step explanation:

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3 0
2 years ago
A thermometer gives a reading of 26 degrees Celsius. Use the formula c =5/9(f-32). Write the inverse function and use it to find
guajiro [1.7K]

Answer:

The answer to your question is F = 78.8

Step-by-step explanation:

Equation

                           C = \frac{5}{9} (F - 32)

Multiply both sides by 9

                           9C = \frac{5(9)}{9} (F - 32)

Simplify

                           9C = 5(F - 32)

Divide both sides by 5

                           \frac{9}{5} C = \frac{5}{5} (F - 32)

Simplify

                           \frac{9}{5} C = F -32

Add 32 in both sides

                           \frac{9}{5} C + 32 = F - 32 + 32

Simplify (Inverse)

                           \frac{9}{5} C + 32 = F

Substitute to find F

                           \frac{9}{5} (26) + 32 = F

Simplify

                                          F = 46.8 + 32

Result

                                          F = 78.8    

6 0
3 years ago
A2 = -8 and a5 = -512<br> Find a10
yawa3891 [41]

Answer:

The value of a₁₀ is -1352

Step-by-step explanation:

a₂ = -8

a₅ = -512

Now,

a₂ = -8 can be written as

a + d = -8 ...(1) and

a₅ = -512 can be written as

a + 4d = -512 ...(2)

Now, from equation (2) we get,

a + 4d = - 512

a + d + 3d = - 512

(-8) + 3d = - 512 (.°. <u>a + d = </u><u>-8</u><u>)</u>

3d = - 512 + 8

3d = - 504

d = - 504 ÷ 3

d = - 168

Now, for the value of a put the value of d = -168 in equation (1)

a + d = -8

a + (-168) = -8

a - 168 = -8

a = 168 - 8

a = 160

Now, For a₁₀

a₁₀ = a + 9d

a₁₀ = 160 + 9(-168)

a₁₀ = 160 - 1512

a₁₀ = -1352

Thus, The value of a₁₀ is -1352

<u>-TheUnknownScientist</u>

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There would be about a 14.3% chance of being able to see it
30 minutes / 210
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