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3 years ago

The function f(x) = 9x +5 is one-to-one. Find an equation for f-'(x), the inverse function.

Mathematics

1 answer:

Gnesinka [82]3 years ago

8 0

Answer:

The inverse function is $f^{-1}(x) = \frac{x - 5}{9}$

Step-by-step explanation:

Inverse function:

Suppose we have a one-to-one function y = f(x). To find it's inverse, we exchange y and x, and then isolate y.

In this question:

$y = 9x + 5$

Exchanging x and y:

$x = 9y + 5$

Isolating y:

$9y = x - 5$

$y = \frac{x - 5}{9}$

$f^{-1}(x) = \frac{x - 5}{9}$

The inverse function is $f^{-1}(x) = \frac{x - 5}{9}$

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Jacob can create an app in 24 hours, but if he works together with a friend they can create an app in 16 hours. How long would i

iogann1982 [59]

Answer:

Time taken by his friend to create the app alone = 48 hours.

Step-by-step explanation:

Hours needed by Jacob to create an app = 24 hours

$\text{One hour work of Jacob = }\frac{1}{24}$

Let hours needed by his friend in creating the app alone = x hours

$\text{So, one hour work of his friend = }\frac{1}{x}$

The both can create the app in 16 hours.

$\implies \frac{1}{24}+\frac{1}{x}=\frac{1}{16}\\\\\implies\frac{1}{x}=\frac{1}{16}-\frac{1}{24}\\\\\implies\frac{1}{x}=\frac{24-16}{24\times 16}\\\\\implies \frac{1}{x}=\frac{1}{48}\\\\\bf\implies x = 48$

Hence, Time taken by his friend to create the app alone = 48 hours.

7 0

3 years ago

Answer???????????????

Harlamova29_29 [7]

the answer correct is (5,3)

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3 years ago

Which point is collinear to the point (0,0)? A) (1,0) B) (3,2) C) (4,1) D) (1,3)

Sonbull [250]

Answer:

All of them are right

Step-by-step explanation:

Are you sure the question was that?

Collinear means that it lies on the same line

Now, from every 2 points passes a unique line

So(0,0) and (3,2) are in a line

(0,0) and (1,0) are in an other line and so on

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3 years ago

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MrMuchimi

Answer:

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2 years ago

Given the piece wise function show below, select all that are true

NeTakaya

Answer:

Option (C) and (D)

Step-by-step explanation:

Given piecewise function is,

f(x) = 2x, x < 1

5, x = 1

$x^{2}$ , x > 1

Option (A),

x = 5 means x > 1

So the function will be,

f(x) = $x^{2}$

f(5) = (5)²

= 25

Therefore, f(5) = 1 is not correct.

Option (B),

x = -2 means x < 1

f(x) = 2x will be applicable.

f(-2) = 2(-2) = -4

Therefore, f(-2) = 4 is not correct.

Option (C)

For x = 1,

f(1) = 5

Therefore, f(1) = 5 is the correct option.

Option (D)

x = 2 means x > 1 and the function defined will be,

f(x) = x²

f(2) = 2²

= 4

Therefore, f(2) = 4 will be the correct option.

Options (C) and (D) will be the answer.

7 0

3 years ago