We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.

+0

# Find the Inverse

+1
238
4
+2448

$$f(n)=\sqrt[5]{n+2}$$

$$f(x)=-2x^3-1$$

Please help!

Oct 29, 2018

### 4+0 Answers

#1
+2448
+3

I got the first one but need help with the second!

Let me know if you would like to see my work~

Oct 29, 2018
#2
+102948
+3

Write the first as

y  =  ( n + 2)^(1/5)      take both sides to the 5th power

y^5  = n + 2       subtract 2 from both sides

y^5  - 2  = n         "swap" n  and y

n^5  - 2  =  y      for y, write  f-1 (n)..so...

f-1(n)  = n^5  - 2

Second one

y  = -2x^3  - 1      add 1 to both sides

y  + 1  =  -2x^3       multiply through by - 1

- (y + 1)  = 2x^3       divide both sides by 2

-(y + 1) / 2  =  x^3        take the cube root of both sides

[ - (y + 1)  / 2 ] ^(1/3)  =  x      "swap "  x  and y

[ - ( x + 1) / 2 ]^(1/3)  =  y      for y, write  f-1(x)

f-1(x)  =  [ - (x + 1) / 2 ] ^(1/3)

Oct 29, 2018
#3
+2448
+2

Thank you

RainbowPanda  Oct 29, 2018
#4
+4322
+2

Yes, instead of f(x), set it to y!

Oct 29, 2018