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2 years ago

Select the correct answer. Find the Inverse of function A F(x)=1/3 -1/2x

Mathematics

1 answer:

kompoz [17]2 years ago

7 0

Answer:

If you actually meant f(x)=2x+3x−1 ,

then note it can be rewritten as:

f(x)=2x−2+5x−1=2+5x−1=y

At this point you can find x in terms of y (“make x the subject”):

y−2=5x−1⟹1y−2=x−15

⟹x=5y−2+1=y+3y−2

Switch variables back to x, and you have the inverse function of f:

g(x)=x+3x−2

How do you know you’ve calculated correctly? The composition of f with g should result in x — that is, evaluate f(g) and you should get the result x:

You might be interested in

A grasshopper jumps straight up from the ground with an initial vertical velocity of 8 feet per second. After how many seconds w

vlabodo [156]

Answer:

Problem 1 : After 0.25 s

Problem 2 : The squirrel doesn't reach the ground before the nut

Step-by-step explanation:

Problem 1

This is a standard physics problem

The equation that defines the movement of the grasshopper given the initial velocity, and the acceleration is the following

Distance = Do + Vo*t + 0.5*a*t^2

Where

Do is the initial distance.

(Do = 0, because the grasshopper is on the ground and we choose the reference system there)

Vo is the initial velocity = 8 feet/sec

a is the acceleration that is exerted on the body (in this case a = g = -9.8 m/s^2 = - 32.174 feet per second per second.)

t is the time

We substitute in the equation, and solve for t (time)

Distance = Do + Vo*t + 0.5*a*t^2

(1 foot)= (0)+ (8 feet/s)*t + 0.5*(-32.174 feet/s^2)*t^2

Solving this equation, we get that

t = 0.25 s

Problem 2

This problem is similar to the previous one

We apply the same formula

D = Do + Vo*t + 0.5*a*t^2

But in this case, we are going in the opposite direction, and we have an initial distance.

Do = 27 feet

Vo is the initial velocity of the nut = -6 feet/s

D = 0 (Ground)

We substitute in the equation, and solve for t (time)

(0) = (27) + (-6 feet/s)*t + 0.5*(-32 feet/s^2)*t^2

t = 1.125 s < 2s

The nut reaches ground in 1.125 s, so the squirrel doesn't reach the ground before the nut

4 0

2 years ago

Find an equation for the perpendicular Bisector of the line segment whose endpoints are (-9,-8) and (7,-4

Alina [70]

equation for the perpendicular Bisector of the line segment whose endpoints are (-9,-8) and (7,-4)

Perpendicular bisector lies at the midpoint of a line

Lets find mid point of (-9,-8) and (7,-4)

midpoint formula is

$\frac{x_1+x_2}{2} ,\frac{y_1+y_2}{2}$

$\frac{-9+7}{2} ,\frac{-8+-4}{2}$

midpoint is (-1, -6)

Now find the slope of the given line

(-9,-8) and (7,-4)

$slope = \frac{y2-y1}{x2-x1} = \frac{-4-(-8)}{7-(-9)}$

$slope = \frac{-4+8}{7+9}= \frac{4}{16} =\frac{1}{4}$

Slope of perpendicular line is negative reciprocal of slope of given line

So slope of perpendicular line is -4

slope = -4 and midpoint is (-1,-6)

y - y1 = m(x-x1)

y - (-6) = -4(x-(-1))

y + 6 = -4(x+1)

y + 6 = -4x -4

Subtract 6 on both sides

y = -4x -4-6

y= -4x -10

equation for the perpendicular Bisector y = -4x - 10

3 0

2 years ago

12a2 + 4b for a = 8 & b = -6.<br> PLease help

ololo11 [35]

Answer:

744

Step-by-step explanation:

12a^2 + 4b

Plug-in:

12(8)^2 + 4(-6)

12(64) + 4(-6)

768 - 24

744

4 0

2 years ago

Sam is proving the product property of logarithms.

Charra [1.4K]

Answer: c

Step-by-step explanation: edge 2021

8 0

2 years ago

Someone help me please!!!!

Ghella [55]

I am pretty sure number 3 is the right answer

8 0

2 years ago