M < TYV=64Â° What is m A.116Â° B.90Â° C.26Â° D.64Â°

Which pair of funtions is not a pair of inverse functions? please help!!

antiseptic1488 [7]

Answer:

$f(x)=\frac{x}{x+20} , g(x)=\frac{20x}{x-1}$

Step-by-step explanation:

we know that

To find the inverse of a function, exchange variables x for y and y for x. Then clear the y-variable to get the inverse function.

we will proceed to verify each case to determine the solution of the problem

case A) $f(x)=\frac{x+1}{6} , g(x)=6x-1$

Find the inverse of f(x)

Let

y=f(x)

Exchange variables x for y and y for x

$x=\frac{y+1}{6}$

Isolate the variable y

$6x=y+1$

$y=6x-1$

Let

$f^{-1}(x)=y$

$f^{-1}(x)=6x-1$

therefore

f(x) and g(x) are inverse functions

case B) $f(x)=\frac{x-4}{19} , g(x)=19x+4$

Find the inverse of f(x)

Let

y=f(x)

Exchange variables x for y and y for x

$x=\frac{y-4}{19}$

Isolate the variable y

$19x=y-4$

$y=19x+4$

Let

$f^{-1}(x)=y$

$f^{-1}(x)=19x+4$

therefore

f(x) and g(x) are inverse functions

case C) $f(x)=x^{5}, g(x)=\sqrt[5]{x}$

Find the inverse of f(x)

Let

y=f(x)

Exchange variables x for y and y for x

$x=y^{5}$

Isolate the variable y

fifth root both members

$y=\sqrt[5]{x}$

Let

$f^{-1}(x)=y$

$f^{-1}(x)=\sqrt[5]{x}$

therefore

f(x) and g(x) are inverse functions

case D) $f(x)=\frac{x}{x+20} , g(x)=\frac{20x}{x-1}$

Find the inverse of f(x)

Let

y=f(x)

Exchange variables x for y and y for x

$x=\frac{y}{y+20}$

Isolate the variable y

$x(y+20)=y$

$xy+20x=y$

$y-xy=20x$

$y(1-x)=20x$

$y=20x/(1-x)$

Let

$f^{-1}(x)=y$

$f^{-1}(x)=20x/(1-x)$

$\frac{20x}{1-x}\neq \frac{20x}{x-1}$

therefore

f(x) and g(x) is not a pair of inverse functions

7 0

3 years ago

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A car is traveling at -40 miles per hour. What will their position be after 3 hours?

marissa [1.9K]

Answer:

-120 miles

Step-by-step explanation:

A car is traveling at -40 miles per hour. What will their position be after 3 hours?

-40 mph times 3 hours is -120 miles

4 0

2 years ago

Twice a number decreased by four is seven

GalinKa [24]

Answer:

2x > 10+4

x > 14/2

x > 7

Step-by-step explanation:

4 0

3 years ago

A 12.3-ounce package costs $2.99. What is the unit price?

IRINA_888 [86]

Answer:

$0.243089430894309 Per ounce

Price divided by ounces gives you the unit price. Since this is an unreal number when talking about price it will be $0.24 per ounce.

3 0

3 years ago

X-1/x^2 - x - 20 Give the equivalent numerator if the denominator is (X - 5)(x + 4)(x + 3)

Fynjy0 [20]

Answer:

$x^2+2x-3$

Step-by-step explanation:

Note that $x^2-x-20=(x-5)(x+4)$ , so, if the denominator is $(x-5)(x+4)(x+3)$ , we need to multiply the numerator by $(x+3)$ . And $(x-1)(x+3)=x^2+2x-3$ .

3 0

2 years ago