Given the function f(x)=4(x+3)-5, solve for the inverse function when x=3.

- Janu16

Given the function f(x)=4(x+3)-5, solve for the inverse function when x=3.

- katieb

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- Janu16

plz help

- Janu16

- Janu16

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## More answers

- anonymous

To find the inverse of a function, you always want to change x and y, then solve for y again.
First, change f(x) to y to avoid any confusion. \[y=4(x+3)-5\]
Now, swap x and y. \[x=4(y+3)-5\]
All you have to do now is solve for y. Once you've done that, substitute 3 in for x, and you'll be all set!

- Janu16

Wait so how do you substitute x for 3?

- Janu16

- Janu16

@nincompoop can you please help?

- Janu16

- geerky42

by plug in x=3

- geerky42

Just replace x to 3.

- Janu16

so it would be x=4(y+3)-5
x=4(3+3)-5?

- Janu16

- DanJS

Are you still working on this ?

- Janu16

yes

- DanJS

f(x) = y = 4(x+3) - 5 is a line that is given
y = 4x + 12 -5
y = 4x + 7

- Janu16

ya so when do you substitute x for 3?

- DanJS

The inverse of that , will be another line that is reflected over the line with slope 1, y=x.
To figure that , you can just switch x and y around and resolve for the new y.

- DanJS

Original: y = 4x + 7
Inverse: x = 4y + 7
x - 7 = 4y
y = (x-7) / 4

- DanJS

Put x=3 in the inverse function, calculate the y value

- Janu16

-1?

- geerky42

That's correct.

- DanJS

##### 1 Attachment

- DanJS

See it is a reflection if you switch the x and y around, as in the graph

- Janu16

ya i see it. it really helped thank you so much and do you know how to do f(g(x) problems?

- DanJS

sure

- Janu16

well i need help with Given that f(x) = x2 + 2x + 3 and g(x) = quantity of x plus four, over three, solve for f(g(x)) when x = 2.

- Janu16

like i dont know how to setup

- DanJS

solve g(2) first, what is that

- DanJS

g(x) = (x+4) / 3

- Janu16

2?

- Janu16

wait do you put 2 for x?

- DanJS

yes, now find f[g(2)], what do ya think to do?

- Janu16

4x2x+3 than 6x=3 which is 2?

- DanJS

since g(2) = 2 , start from the middle and work outwards
f(2) = 2^2 + 2*2 + 3

- Janu16

11?

- DanJS

yeah

- Janu16

oh i forgot to substitute x with 2 for 2x

- Janu16

so if i haveanother problem like in future do i solve g first? or depending on the problem

- DanJS

for compound functions like f([g(x)] start with the inner function, evaluate if given a value, then use g(x) value in f(x)...
work inner function to outer functions

- Janu16

ohok thank you very much!

- DanJS

welcome, goodluck

- Janu16

there are like some problems like f(x) and g(x) and you have to compare them. there are lot of problems but i dont know how to compare like if you know how to do it i will put it on new page

- DanJS

sure, just tag my name with @name

- Janu16

ok thanks

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