2. Consider the function f(x)=1/4 x+2.

a. Find the inverse of f(x) and name it g(x). Show and explain your work.

b. Use function composition to show that f(x) and g(x) are inverses of each other.

Question

2.	Consider the function  f(x)=1/4 x+2.

a.	Find the inverse of f(x) and name it g(x). Show and explain your work.







b.	Use function composition to show that f(x) and g(x) are inverses of each other.

anonymous · Answer

Have you tried it yourself?

annie96 · Answer

Yes

anonymous · Answer

Do you have real picture of it or it it on paper?

annie96 · Answer

it doesn't have a picture it's on paper.

anonymous · Answer

Is this a inverse function for f(x) and g(x). Can I have a picture by possible?

anonymous · Answer

I'll just start doing it then.

fibonaccichick666 · Answer

can you show us your work to begin please?

annie96 · Answer

f^−1(x)=4x−8

fibonaccichick666 · Answer

I agree, so that is our g(x)

fibonaccichick666 · Answer

so, now, I bet austin can tell you what function composition is, let's allow him part b.

annie96 · Answer

@FibonacciChick666 do I put g instead of f?

anonymous · Answer

Replace f(x) with y.
y=$$y=\frac{ 1 }{ 4}\times x + 2$$

Interchange the variables.
$$x=\frac{ 1 }{ 4 }\times y + 2$$

Since y is on the right-hand side of the equation, siwtch the sides so it is on the left hand side of the equation.
$$\frac{ 1 }{ 4}\times y + 2 =x$$
Multiply$$\frac{ 1 }{ 4 }$$ by Y to get $$(\frac{ 1 }{ 4 })y$$
$$(\frac{ 1 }{ 4 })y+2=x$$

Simplify $$(\frac{ 1 }{ 4 })y$$
$$\frac{ y }{ 4 }+2=x$$

Since 2 does not contain the variable to solve for, move it to the right-hand side of the equation by subtracting 2 from both sides.
$$\frac{ y }{ 4 }=-2+x$$

Multiply both sides of the equation by 4.
$$y=-2\times(4)+x \times(4)$$

Multiply -2 by 4 to get -8.
$$y=-8+x \times(4)$$

Multiply x by 4 to get x(4).
$$y=-8+x(4)$$
Multiply x by 4 to get $$x \times 4$$
$$y=-8+x \times 4$$

Move 4 to the left of the expression $$x \times 4$$
$$y=-8+4\times x$$

Multiply 4 by x to get 4x
$$y=-8 + 4x$$

Reorder -8 and 4x.
$$y=4x-8$$

$$y=4x-8$$

@Annie96

anonymous · Answer

Do you understand it so far

annie96 · Answer

Yes Thank You.

anonymous · Answer

Do you need more

anonymous · Answer

Hold on I need to show you more that might change your answer give me like 5 minutes plz

annie96 · Answer

okay

fibonaccichick666 · Answer

oh, yea, you are just renaming f^-1 as g since it's easier to write

annie96 · Answer

okay

fibonaccichick666 · Answer

it's like giving it a nickname

fibonaccichick666 · Answer

now, do you know how to compose functions?  Do you know what that means?

anonymous · Answer

Replace y with $$f-1(x).$$

$$f-1(x)=4x-8$$

Setup the composite result function. The f o g notation is interpreted as f(g(x)).
$$f(g(x))$$

Evalute f(g(x)) by substituting in the value of g into f.
$$f(4x-8)=\frac{ 1 }{ 4 }\times (4x-8) + 2$$

Multiply 1/4 by 4x-8 to get (1/4)(4x-8).
$$f(4x-8)=(\frac{ 1 }{ 4 })(4x-8)+2$$

Apply the distributive property.
$$f(4x-8)=(\frac{ 1 }{ 1 })(\frac{ x }{ 1 })+(\frac{ 1 }{ 4 })(-8)+2$$

Simplify.
$$f(4x-8)=x+(\frac{ 1 }{ 4 })(-8)+2$$

Simplify(1/4)(-8)
$$f(4x-8)=x+\frac{ -8 }{ 4}+2$$

Divide -8 by 4 to get -2. 
$$f(4x-8)=x-2+2$$

Add-2 and 2 to get 0.
$$f(4x-8)=x+0$$

Add x and 0 to get x
$$f(4x-8)=x$$

Since f(g(x)) - x,f-1(x)=4x-8 is the inverse of f(x) =1/4x X+2
$$f-1(x)=4x-8$$

$$g-1(x)=4x-8$$

I renamed f(x) as g(x) so this should help your answers.

anonymous · Answer

@Annie96

anonymous · Answer

I did detailed instructions with inverse functions for f(x) and g(x) so  you should understand this and figure this out.

annie96 · Answer

thank you

anonymous · Answer

I can help you figure out more questions like this or depends on the questions.

anonymous · Answer

A. I did tons of work and details for f(x) and g(x).
B. Gave you the f(x) and g(x) functions

annie96 · Answer

thank you