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3 years ago

What is the inverse of the function f(x)=4x+8

Mathematics

1 answer:

Leno4ka [110]3 years ago

7 0

Answer:

f ( x ) − 1 = ( 1/ 4 x ) − 2.

Step-by-step explanation:

For inverse function, the x and y interchanges and then make y the subject again of the equation. See the working out below:

f ( x ) = 4 x + 8

f ( x ) = y

y = 4 x + 8

x = 4 y + 8 ----- interchanging y and x

Now make y the subject of the equation:

x = 4 y + 8

− 4 y = - x + 8

y = ( − 1/ 4 ) . − x + ( − 1/ 4 ) .8

y = ( 1/ 4 x ) − 2

So the inverse function is:

f (x) − 1 = ( 1/ 4 x ) − 2

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Ksju [112]

Answer:

$\frac{5}{12}$

Step-by-step explanation:

The given problem is a subtraction problem between fractions. The first step in a problem like this is to convert both fractions to a common denominator. In other words, multiply both the numerator and denominator of a fraction by the same value such that the denominator of one of the fractions is the same as the other fraction. The numerator of a fraction is the value over the fraction bar, whereas the denominator is the value under it. Multiplying any fraction by a number over itself is the same as multiplying it by one, thus, the equation will remain true, and be equivalent to the original expression.

$\frac{13}{12}-\frac{2}{3}$

Convert to a common denominator,

$\frac{13}{12}-(\frac{2}{3}*\frac{4}{4})$

$\frac{13}{12}-\frac{8}{12}$

Now perform the subtraction, subtract one numerator from the other, remember, do no perfrom any more operations with the denominators,

$\frac{5}{12}$

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Step-by-step explanation:

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3 years ago

Read 2 more answers

Find the area of a circle with radius 6m use the value 3.14

Umnica [9.8K]

Area= 3.14 x 6squared
= 113.04m

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3 years ago

Read 2 more answers

f(x) = 3 cos(x) 0 ≤ x ≤ 3π/4 evaluate the Riemann sum with n = 6, taking the sample points to be left endpoints. (Round your ans

Kruka [31]

Answer:

$\int_{0}^{\frac{3 \pi}{4}}3 \cos{\left(x \right)}\ dx\approx 3.099558$

Step-by-step explanation:

We want to find the Riemann sum for $\int_{0}^{\frac{3 \pi}{4}}3 \cos{\left(x \right)}\ dx$ with n = 6, using left endpoints.

The Left Riemann Sum uses the left endpoints of a sub-interval:

$\int_{a}^{b}f(x)dx\approx\Delta{x}\left(f(x_0)+f(x_1)+2f(x_2)+...+f(x_{n-2})+f(x_{n-1})\right)$

where $\Delta{x}=\frac{b-a}{n}$ .

Step 1: Find $\Delta{x}$

We have that $a=0, b=\frac{3\pi }{4}, n=6$

Therefore, $\Delta{x}=\frac{\frac{3 \pi}{4}-0}{6}=\frac{\pi}{8}$

Step 2: Divide the interval $\left[0,\frac{3 \pi}{4}\right]$ into n = 6 sub-intervals of length $\Delta{x}=\frac{\pi}{8}$

$a=\left[0, \frac{\pi}{8}\right], \left[\frac{\pi}{8}, \frac{\pi}{4}\right], \left[\frac{\pi}{4}, \frac{3 \pi}{8}\right], \left[\frac{3 \pi}{8}, \frac{\pi}{2}\right], \left[\frac{\pi}{2}, \frac{5 \pi}{8}\right], \left[\frac{5 \pi}{8}, \frac{3 \pi}{4}\right]=b$

Step 3: Evaluate the function at the left endpoints

$f\left(x_{0}\right)=f(a)=f\left(0\right)=3=3$

$f\left(x_{1}\right)=f\left(\frac{\pi}{8}\right)=3 \sqrt{\frac{\sqrt{2}}{4} + \frac{1}{2}}=2.77163859753386$

$f\left(x_{2}\right)=f\left(\frac{\pi}{4}\right)=\frac{3 \sqrt{2}}{2}=2.12132034355964$

$f\left(x_{3}\right)=f\left(\frac{3 \pi}{8}\right)=3 \sqrt{\frac{1}{2} - \frac{\sqrt{2}}{4}}=1.14805029709527$

$f\left(x_{4}\right)=f\left(\frac{\pi}{2}\right)=0=0$

$f\left(x_{5}\right)=f\left(\frac{5 \pi}{8}\right)=- 3 \sqrt{\frac{1}{2} - \frac{\sqrt{2}}{4}}=-1.14805029709527$

Step 4: Apply the Left Riemann Sum formula

$\frac{\pi}{8}(3+2.77163859753386+2.12132034355964+1.14805029709527+0-1.14805029709527)=3.09955772805315$

$\int_{0}^{\frac{3 \pi}{4}}3 \cos{\left(x \right)}\ dx\approx 3.099558$

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Answer:

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Step-by-step explanation:

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