Mathematics, 27.11.2019 04:31 chem1014

What is the inverse of the function f(x) = 1/4x – 12?

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To find the inverse all you do is swap your x and y then solve it through. for this one you gotta take f(x) and make it y

y = 1/4x - 12

then swap

x = 1/4y - 12

then solve it through

x - 12 = 1/4y

divide by (1/4)

and (x - 12)4 = y should be your answer

Answer from: gizmo50245

To answer this, you want to start by changing 'f(x)' to 'x', and 'x' to the inverse function - let's call it 'g(x)'. This is inverting the function - it's like swapping the x and y axes around. That will give you: x = 1/4g(x) - 12

Now you want to rearrange that equation to put g(x) on the left hand side. That's not so hard to do - although I'm not sure if the question is (1/4)x or 1/(4x), so I'll answer for both:

x + 12 = (1/4)g(x)
4x + 48 = g(x)
g(x) = 4x + 48

or, if the question is 1/(4x):
x + 12 = 1/(4g(x))
1/(x + 12) = 4g(x)
1/(4x + 48) = g(x)
g(x) = 1/(4x + 48)

Answer from: Quest

step-by-step explanation:

Answer from: Quest

let's add {f(x)=x+1}f(x)=x+1 and {g(x)=2x}g(x)=2x together to make a new function.

f(x)+g(x) =(x+1)+(2x)=x+1+2x=3x+1

let's call this new function hh. so we have:

{h(x)}={f(x)}+{g(x)}{=3x+1}h(x)=f(x)+g(x)=3x+1

we can also evaluate combined functions for particular inputs. let's evaluate function hh above for x=2x=2. below are two ways of doing this.

method 1: substitute x=2x=2 into the combined function hh.

h(x)

h(2)

=3x+1

=3(2)+1

since h(x)=f(x)+g(x)h(x)=f(x)+g(x), we can also find h(2)h(2) by finding f(2) +g(2)f(2)+g(2).

first, let's find f(2)f(2):

f(x)

f(2)

=x+1

=2+1

now, let's find g(2)g(2):

g(x)

g(2)

=2x

=2⋅2

so f(2)+g(2)=3+4=\greend7f(2)+g(2)=3+4=7.

notice that substituting x =2x=2 directly into function hh and finding f(2) + g(2)f(2)+g(2) gave us the same answer!

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